Question 1

Ron and Kathy are ticket-sellers at their class play. Ron is selling student tickets for $\$ 3.00$ each, and Kathy selling adult tickets for $\$ 5.50$ each. If their total income for 19 tickets was $\$ 72.00$, how many tickets did Ron sell?

Accepted Answer

The answer of Ron and Kathy are ticket-sellers at their...

Question 2

There were 600 people at a play. The admission price was $\$ 2$ for adults and $\$ 1$ for children. The admission receipts were $\$ 920$. How many adults and how many children attended?

Accepted Answer

Let the number of adults be $a$ and the number of children be $c$. We have two equations: $a + c = 600$ (total number of people) and $2a + c = 920$ (total admission receipts). Solving these equations simultaneously gives $a = 320$ and $c = 280$.

Question 3

Don runs a charity fruit sale, selling boxes of oranges for $\$ 11$ and boxes of grapefruit for $\$ 10$. If he sold a total of 762 boxes and took in $\$ 8125$ in all, then how many boxes of oranges did he sell?

Accepted Answer

The answer of Don runs a charity fruit sale, selling...

Question 4

Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $\$ 105.00$ for 3 days and 300 miles, while Mary was charged $\$ 195.00$ for 5 days and 600 miles. What does Best Rentals charge per day and per mile?

Accepted Answer

Let $x$ be the daily charge and $y$ be the charge per mile. From the given information, we have two equations: $3x + 300y = 105$ and $5x + 600y = 195$. Solving these equations simultaneously, we find $x = 15$ and $y = 0.20$, which means $\$15$ per day and $\$0.20$ per mile.

Question 5

35,000 people attended a ballgame at a stadium that offers two kinds of seats: general admission and reserved. The day's receipts were $\$ 236,000$. How many people paid $\$ 12.00$ for reserved seats, and how many paid $\$ 4.00$ for general admission?

Accepted Answer

Let $x$ be the number of reserved seats and $y$ be the number of general admission seats. We have two equations: $x + y = 35,000$ (total number of people) and $12x + 4y = 236,000$ (total receipts). Solving these equations simultaneously gives $x = 12,000$ and $y = 23,000$.

Question 6

Ellen wishes to mix candy worth $\$ 2.12$ per pound with candy worth $\$ 3.71$ per pound to form 26 pounds of a mixture worth $\$ 2.73$ per pound. How many pounds of the more expensive candy should she use?

Accepted Answer

Ellen can use the equation $2.12x + 3.71(26-x) = 2.73(26)$ to find the amount of the more expensive candy. Solving for $x$ gives the amount of the cheaper candy, and subtracting from 26 gives the amount of the more expensive candy, which is 10 pounds.

Question 7

A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with $4 \%$ cement should he mix with 3 bags of $44 \%$ cement to produce a mix containing $12 \%$ cement?

Accepted Answer

The answer of A contractor mixes concrete from bags of...

Question 8

Anne and Nancy use a metal alloy that is $19 \%$ copper to make jewelry. How many ounces of an alloy that is $12 \%$ copper must be mixed with an alloy that is $25 \%$ copper to form 65 ounces of the desired alloy?

Accepted Answer

Let $x$ be the amount of the $12\%$ copper alloy, and $65 - x$ be the amount of the $25\%$ copper alloy. The equation to represent the mixture is $0.12x + 0.25(65 - x) = 0.19 \times 65$. Solving for $x$ gives $x = 30$ ounces.

Question 9

How many liters (L) of a $40 \%$ alcohol solution must be mixed with $60 \mathrm{~L}$ of a $60 \%$ solution to get a $50 \%$ solution?

Accepted Answer

To achieve a $50\%$ solution when mixing a $40\%$ solution with a $60\%$ solution, equal amounts of each must be mixed. Therefore, $60 \mathrm{~L}$ of the $40\%$ solution is needed to match the $60 \mathrm{~L}$ of the $60\%$ solution.

Question 10

How many liters (L) of a $10 \%$ silver iodide solution must be mixed with $5 \mathrm{~L}$ of a $4 \%$ silver iodide solution to get a $6 \%$ solution?

Accepted Answer

To find the correct amount, we can use the equation for mixture problems: $C_1V_1 + C_2V_2 = C_{final}(V_1 + V_2)$, where $C_1$ and $C_2$ are the concentrations of the initial solutions, $V_1$ and $V_2$ are the volumes of the initial solutions, and $C_{final}$ is the concentration of the final solution. Plugging in the given values: $0.10V_1 + 0.04(5) = 0.06(V_1 + 5)$. Solving for $V_1$ gives $V_1 = 2.5$ liters.

Question 11

A merchant has coffee worth $\$ 40$ a pound that she wishes to mix with 60 pounds of coffee worth $\$$ 80 a pound to get a mixture that is worth $\$ 70$ a pound. How many pounds (lb) of the $\$ 40$ coffee should be used?

Accepted Answer

To find the amount of $40 coffee needed, set up the equation: $40x + 80(60) = 70(x + 60)$. Solving for $x$, we get $x = 20$ pounds.

Question 12

A cruise boat travels 36 miles downstream in 3 hours and returns to its starting point upstream in 6 hours. Find the speed of the stream.

Accepted Answer

The speed of the stream can be found by calculating the difference between the boat's speed in still water and its speed relative to the ground, then dividing by 2. The boat's speed downstream is $36 \, \text{miles} / 3 \, \text{hours} = 12 \, \text{mph}$, and upstream is $36 \, \text{miles} / 6 \, \text{hours} = 6 \, \text{mph}$. The boat's speed in still water would be the average of these two speeds, $ (12 + 6) / 2 = 9 \, \text{mph}$. The speed of the stream is the difference between the boat's speed in still water and its speed upstream or downstream, so $12 - 9 = 3 \, \text{mph}$ or $9 - 6 = 3 \, \text{mph}$.

Question 13

The speed of a stream is $6 \mathrm{mph}$. If a boat travels 54 miles downstream in the same time that it takes to travel 27 miles upstream, what is the speed of the boat in still water?

Accepted Answer

The speed of the boat in still water is $x$. Downstream speed is $x + 6$ and upstream speed is $x - 6$. The time taken for both journeys is the same, so $\frac{54}{x+6} = \frac{27}{x-6}$. Solving this equation gives $x = 18$.

Question 14

A plane flies 500 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is $24 \mathrm{mph}$, what is the speed of the plane in still air?

Accepted Answer

Let the speed of the plane in still air be $x$ mph. When flying with the wind, the plane's speed is $x + 24$ mph, and against the wind, it's $x - 24$ mph. Since the times for both parts of the trip are the same, we can set up the equation $\frac{500}{x + 24} = \frac{350}{x - 24}$. Solving this equation for $x$ gives the speed of the plane in still air as $136$ mph.

Question 15

An airplane travels 800 miles against the wind in 5 hours, and makes the return trip with the same wind in 2 hours. Find the rate of the wind.

Accepted Answer

The airplane's speed against the wind is $ \frac{800}{5} = 160 $ mph, and with the wind is $ \frac{800}{2} = 400 $ mph. Let $ p $ be the plane's speed in still air and $ w $ be the wind speed. Then, $ p - w = 160 $ and $ p + w = 400 $. Solving these equations, we find $ w = 120 $ mph.

Question 16

John and Tony start from Grays lake at the same time and head for a town 10 miles away. John walks twice as fast as Tony and arrives 3 hours before Tony. Find how fast each walks.

Accepted Answer

Let Tony's speed be $ x $ mph. Then John's speed is $ 2x $ mph. The time taken by Tony is $ \frac{10}{x} $ hours and by John is $ \frac{10}{2x} = \frac{5}{x} $ hours. Since John arrives 3 hours before Tony, we have $ \frac{10}{x} - \frac{5}{x} = 3 $. Solving this gives $ x = \frac{5}{3} $ mph for Tony and $ 2x = \frac{10}{3} $ mph for John.

Question 17

From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 11 miles per hour. In how many hours will they be 63 miles apart?

Accepted Answer

Since the boats are moving in opposite directions, their speeds add up. Therefore, their combined speed is 10 + 11 = 21 miles per hour. To find the time it takes for them to be 63 miles apart, divide the distance by their combined speed: 63 / 21 = 3 hours.

Question 18

A cabin cruiser travels 20 miles in the same time that a power boat travels 40 miles. The cruiser travels $5 \mathrm{mph}$ slower than the power boat. Find the speed of each boat.

Accepted Answer

The answer of A cabin cruiser travels 20 miles in...

Question 19

An express train and a local train both leave Gray's Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train.

Accepted Answer

The express train travels twice as fast as the local train and arrives 1 hour earlier. If the local train's speed is $x$, then the express train's speed is $2x$. The local train takes $\frac{50}{x}$ hours, and the express train takes $\frac{50}{2x}$ hours. The difference in time is 1 hour: $\frac{50}{x} - \frac{50}{2x} = 1$. Solving this equation gives $x = 25$, so the local train's speed is $25 \mathrm{mph}$ and the express train's speed is $50 \mathrm{mph}$.

Question 20

Candy and Delvis are riding bicycles in the same direction. Candy rides at a speed of 3 miles per hour, and Delvis rides at a speed of 9 miles per hour. If they started at the same place (and at the same time), then after 5 hours what is the distance between them?

Accepted Answer

In 5 hours, Candy will have traveled 5 * 3 = 15 miles, and Delvis will have traveled 5 * 9 = 45 miles. The distance between them is 45 - 15 = 30 miles.

Quiz 4: Systems of Linear Equations

Ron and Kathy are ticket-sellers at their class play. Ron is selling student tickets for $\$ 3.00$ each, and Kathy selling adult tickets for $\$ 5.50$ each. If their total income for 19 tickets was $\$ 72.00$ , how many tickets did Ron sell?

There were 600 people at a play. The admission price was $\$ 2$ for adults and $\$ 1$ for children. The admission receipts were $\$ 920$ . How many adults and how many children attended?

Don runs a charity fruit sale, selling boxes of oranges for $\$ 11$ and boxes of grapefruit for $\$ 10$ . If he sold a total of 762 boxes and took in $\$ 8125$ in all, then how many boxes of oranges did he sell?

Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $\$ 105.00$ for 3 days and 300 miles, while Mary was charged $\$ 195.00$ for 5 days and 600 miles. What does Best Rentals charge per day and per mile?

35,000 people attended a ballgame at a stadium that offers two kinds of seats: general admission and reserved. The day's receipts were $\$ 236,000$ . How many people paid $\$ 12.00$ for reserved seats, and how many paid $\$ 4.00$ for general admission?

Ellen wishes to mix candy worth $\$ 2.12$ per pound with candy worth $\$ 3.71$ per pound to form 26 pounds of a mixture worth $\$ 2.73$ per pound. How many pounds of the more expensive candy should she use?

A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with $4 \%$ cement should he mix with 3 bags of $44 \%$ cement to produce a mix containing $12 \%$ cement?

Anne and Nancy use a metal alloy that is $19 \%$ copper to make jewelry. How many ounces of an alloy that is $12 \%$ copper must be mixed with an alloy that is $25 \%$ copper to form 65 ounces of the desired alloy?

How many liters (L) of a $40 \%$ alcohol solution must be mixed with $60 \mathrm{~L}$ of a $60 \%$ solution to get a $50 \%$ solution?

How many liters (L) of a $10 \%$ silver iodide solution must be mixed with $5 \mathrm{~L}$ of a $4 \%$ silver iodide solution to get a $6 \%$ solution?

A merchant has coffee worth $\$ 40$ a pound that she wishes to mix with 60 pounds of coffee worth $\$$ 80 a pound to get a mixture that is worth $\$ 70$ a pound. How many pounds (lb) of the $\$ 40$ coffee should be used?

A cruise boat travels 36 miles downstream in 3 hours and returns to its starting point upstream in 6 hours. Find the speed of the stream.

The speed of a stream is $6 \mathrm{mph}$ . If a boat travels 54 miles downstream in the same time that it takes to travel 27 miles upstream, what is the speed of the boat in still water?

A plane flies 500 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is $24 \mathrm{mph}$ , what is the speed of the plane in still air?

An airplane travels 800 miles against the wind in 5 hours, and makes the return trip with the same wind in 2 hours. Find the rate of the wind.

John and Tony start from Grays lake at the same time and head for a town 10 miles away. John walks twice as fast as Tony and arrives 3 hours before Tony. Find how fast each walks.

From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 11 miles per hour. In how many hours will they be 63 miles apart?

A cabin cruiser travels 20 miles in the same time that a power boat travels 40 miles. The cruiser travels $5 \mathrm{mph}$ slower than the power boat. Find the speed of each boat.

An express train and a local train both leave Gray's Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train.

Candy and Delvis are riding bicycles in the same direction. Candy rides at a speed of 3 miles per hour, and Delvis rides at a speed of 9 miles per hour. If they started at the same place (and at the same time) , then after 5 hours what is the distance between them?

Quiz 4: Systems of Linear Equations

Ron and Kathy are ticket-sellers at their class play. Ron is selling student tickets for $3.00\$ 3.00$3.00 each, and Kathy selling adult tickets for $5.50\$ 5.50$5.50 each. If their total income for 19 tickets was $72.00\$ 72.00$72.00 , how many tickets did Ron sell?

There were 600 people at a play. The admission price was $2\$ 2$2 for adults and $1\$ 1$1 for children. The admission receipts were $920\$ 920$920 . How many adults and how many children attended?

Don runs a charity fruit sale, selling boxes of oranges for $11\$ 11$11 and boxes of grapefruit for $10\$ 10$10 . If he sold a total of 762 boxes and took in $8125\$ 8125$8125 in all, then how many boxes of oranges did he sell?

Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $105.00\$ 105.00$105.00 for 3 days and 300 miles, while Mary was charged $195.00\$ 195.00$195.00 for 5 days and 600 miles. What does Best Rentals charge per day and per mile?

35,000 people attended a ballgame at a stadium that offers two kinds of seats: general admission and reserved. The day's receipts were $236,000\$ 236,000$236,000 . How many people paid $12.00\$ 12.00$12.00 for reserved seats, and how many paid $4.00\$ 4.00$4.00 for general admission?

Ellen wishes to mix candy worth $2.12\$ 2.12$2.12 per pound with candy worth $3.71\$ 3.71$3.71 per pound to form 26 pounds of a mixture worth $2.73\$ 2.73$2.73 per pound. How many pounds of the more expensive candy should she use?

A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with 4%4 \%4% cement should he mix with 3 bags of 44%44 \%44% cement to produce a mix containing 12%12 \%12% cement?

Anne and Nancy use a metal alloy that is 19%19 \%19% copper to make jewelry. How many ounces of an alloy that is 12%12 \%12% copper must be mixed with an alloy that is 25%25 \%25% copper to form 65 ounces of the desired alloy?

How many liters (L) of a 40%40 \%40% alcohol solution must be mixed with 60 L60 \mathrm{~L}60 L of a 60%60 \%60% solution to get a 50%50 \%50% solution?

How many liters (L) of a 10%10 \%10% silver iodide solution must be mixed with 5 L5 \mathrm{~L}5 L of a 4%4 \%4% silver iodide solution to get a 6%6 \%6% solution?

A merchant has coffee worth $40\$ 40$40 a pound that she wishes to mix with 60 pounds of coffee worth $\$$ 80 a pound to get a mixture that is worth $70\$ 70$70 a pound. How many pounds (lb) of the $40\$ 40$40 coffee should be used?

A cruise boat travels 36 miles downstream in 3 hours and returns to its starting point upstream in 6 hours. Find the speed of the stream.

The speed of a stream is 6mph6 \mathrm{mph}6mph . If a boat travels 54 miles downstream in the same time that it takes to travel 27 miles upstream, what is the speed of the boat in still water?

A plane flies 500 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is 24mph24 \mathrm{mph}24mph , what is the speed of the plane in still air?

An airplane travels 800 miles against the wind in 5 hours, and makes the return trip with the same wind in 2 hours. Find the rate of the wind.

John and Tony start from Grays lake at the same time and head for a town 10 miles away. John walks twice as fast as Tony and arrives 3 hours before Tony. Find how fast each walks.

From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 11 miles per hour. In how many hours will they be 63 miles apart?

A cabin cruiser travels 20 miles in the same time that a power boat travels 40 miles. The cruiser travels 5mph5 \mathrm{mph}5mph slower than the power boat. Find the speed of each boat.

An express train and a local train both leave Gray's Lake at 3 P.M. and head for Chicago 50 miles away. The express travels twice as fast as the local and arrives 1 hour ahead of the local. Find the speed of each train.

Candy and Delvis are riding bicycles in the same direction. Candy rides at a speed of 3 miles per hour, and Delvis rides at a speed of 9 miles per hour. If they started at the same place (and at the same time) , then after 5 hours what is the distance between them?

Ron and Kathy are ticket-sellers at their class play. Ron is selling student tickets for $\$ 3.00$ each, and Kathy selling adult tickets for $\$ 5.50$ each. If their total income for 19 tickets was $\$ 72.00$ , how many tickets did Ron sell?

There were 600 people at a play. The admission price was $\$ 2$ for adults and $\$ 1$ for children. The admission receipts were $\$ 920$ . How many adults and how many children attended?

Don runs a charity fruit sale, selling boxes of oranges for $\$ 11$ and boxes of grapefruit for $\$ 10$ . If he sold a total of 762 boxes and took in $\$ 8125$ in all, then how many boxes of oranges did he sell?

Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $\$ 105.00$ for 3 days and 300 miles, while Mary was charged $\$ 195.00$ for 5 days and 600 miles. What does Best Rentals charge per day and per mile?

35,000 people attended a ballgame at a stadium that offers two kinds of seats: general admission and reserved. The day's receipts were $\$ 236,000$ . How many people paid $\$ 12.00$ for reserved seats, and how many paid $\$ 4.00$ for general admission?

Ellen wishes to mix candy worth $\$ 2.12$ per pound with candy worth $\$ 3.71$ per pound to form 26 pounds of a mixture worth $\$ 2.73$ per pound. How many pounds of the more expensive candy should she use?

A contractor mixes concrete from bags of pre-mix for small jobs. How many bags with $4 \%$ cement should he mix with 3 bags of $44 \%$ cement to produce a mix containing $12 \%$ cement?

Anne and Nancy use a metal alloy that is $19 \%$ copper to make jewelry. How many ounces of an alloy that is $12 \%$ copper must be mixed with an alloy that is $25 \%$ copper to form 65 ounces of the desired alloy?

How many liters (L) of a $40 \%$ alcohol solution must be mixed with $60 \mathrm{~L}$ of a $60 \%$ solution to get a $50 \%$ solution?

How many liters (L) of a $10 \%$ silver iodide solution must be mixed with $5 \mathrm{~L}$ of a $4 \%$ silver iodide solution to get a $6 \%$ solution?

A merchant has coffee worth $\$ 40$ a pound that she wishes to mix with 60 pounds of coffee worth $\$$ 80 a pound to get a mixture that is worth $\$ 70$ a pound. How many pounds (lb) of the $\$ 40$ coffee should be used?

The speed of a stream is $6 \mathrm{mph}$ . If a boat travels 54 miles downstream in the same time that it takes to travel 27 miles upstream, what is the speed of the boat in still water?

A plane flies 500 miles with the wind and 350 miles against the wind in the same length of time. If the speed of the wind is $24 \mathrm{mph}$ , what is the speed of the plane in still air?

A cabin cruiser travels 20 miles in the same time that a power boat travels 40 miles. The cruiser travels $5 \mathrm{mph}$ slower than the power boat. Find the speed of each boat.