Question 1

Solve the percent problem.
-After receiving a discount of $13.5 \%$ on its bulk order of typewriter ribbons, John's Office Supply pays $\$ 6920$. What was the price of the order before the discount?

Accepted Answer

To find the original price before the discount, let $ x $ be the original price. After a 13.5% discount, John pays 86.5% of the original price, so $ 0.865x = 6920 $. Solving for $ x $, we get $ x = \frac{6920}{0.865} = 8000 $.

Question 2

Solve the percent problem.
-After spending $\$ 3650$ for tables and $\$ 3250$ for chairs, a convention center manager finds that $15 \%$ of his original budget remains. Find the amount that remains. Round your answer to the nearest dollar, if necessary.

Accepted Answer

The answer of Solve the percent problem.
-After spending $\$ 3650$...

Question 3

Solve the percent problem.
-Midtown Antiques collects $6 \%$ sales tax on all sales. If total sales including tax are $\$ 1754.33$, find the portion that is the tax. Round your answer to the nearest cent.

Accepted Answer

The total amount including tax is represented as 106% of the original price (100% original + 6% tax). To find the tax portion, we first find the original price by dividing the total by 1.06. Then, we calculate 6% of this original price to find the tax. $ \$1754.33 / 1.06 = \$1655.03 $ as the original price. The tax is $ \$1754.33 - \$1655.03 = \$99.30 $.

Question 4

Solve the investment problem.
-Mardi received an inheritance of $\$ 40,000$. She invested part at $12 \%$ and deposited the remainder in tax-free bonds at $7 \%$. Her total annual income from the investments was $\$ 4300$. Find the amount invested at $12 \%$.

Accepted Answer

Let $x$ be the amount invested at $12\%$, and $40,000 - x$ be the amount invested at $7\%$. The total income is the sum of the incomes from both investments: $0.12x + 0.07(40,000 - x) = 4,300$. Solving this equation for $x$ gives $x = 30,000$.

Question 5

Solve the investment problem.
-Walt made an extra $\$ 5000$ last year from a part-time job. He invested part of the money at $10 \%$ and the rest at $8 \%$. He made a total of $\$ 420$ in interest. How much was invested at $8 \%$ ?

Accepted Answer

Walt invested a total of $5000. Let x be the amount invested at 10%, then $5000 - x is the amount invested at 8%. The interest from these investments is $420. The equation is $0.10x + 0.08(5000 - x) = 420$. Solving for x gives $1000 at 10%, so $4000 at 8%.

Question 6

Solve the investment problem.
-Roberto invested some money at $8 \%$, and then invested $\$ 2000$ more than twice this amount at $10 \%$. His total annual income from the two investments was $\$ 3560$. How much was invested at $10 \%$ ?

Accepted Answer

The answer of Solve the investment problem.
-Roberto invested some money...

Question 7

Solve the investment problem.
-A merchant has coffee worth $\$ 5$ a pound that she wishes to mix with 80 pounds of coffee worth $\$ 8$ a pound to get a mixture worth $\$ 7$ a pound. How many pounds of the $\$ 5$ coffee should be used?

Accepted Answer

The total value of the mixture is calculated by the equation: $5x + 8(80) = 7(x + 80)$, where $x$ is the amount of \$5 coffee. Solving for $x$ gives $x = 40$.

Question 8

Solve the problem.
-Jay drove 268 kilometers at the average rate of 67 kilometers per hour. How long did the trip take?

Accepted Answer

To find the time, divide the total distance by the speed: 268 km / 67 km/h = 4 hours.

Question 9

Solve the problem.
-Janet drove 360 kilometers and the trip took 5 hours. How fast was Janet traveling?

Accepted Answer

To find the speed, divide the total distance by the total time: 360 kilometers / 5 hours = 72 kilometers per hour.

Question 10

Solve the problem.
-What amount of money is found in a coin purse containing 21 dimes and 15 quarters?

Accepted Answer

The total amount is calculated by multiplying the number of each type of coin by its value: 21 dimes (0.10 each) = $2.10 and 15 quarters (0.25 each) = $3.75. Adding these gives $5.85.

Question 11

Solve the problem.
-An equilateral triangle has perimeter 69 inches. What would be the perimeter of a square whose sides each measure the same length as the side of the triangle?

Accepted Answer

The perimeter of the equilateral triangle is 69 inches, so each side is 69 / 3 = 23 inches. A square with sides of the same length would have a perimeter of 4 * 23 = 92 inches.

Question 12

Solve the problem.
-A convention manager finds that she has $\$ 1310$, made up of twenties and fifties. She has a total of 43 bills. How many fifty-dollar bills does the manager have?

Accepted Answer

Let the number of fifty-dollar bills be $x$ and the number of twenty-dollar bills be $y$. We have two equations: $50x + 20y = 1310$ and $x + y = 43$. Solving these equations simultaneously, we find $x = 15$, meaning the manager has 15 fifty-dollar bills.

Question 13

Solve the problem.
-A woman has $\$ 1.70$ in dimes and nickels. She has 2 more dimes than nickels. How many nickels does she have?

Accepted Answer

Let the number of nickels be $n$ and the number of dimes be $d$. Given that $d = n + 2$. Each nickel is worth $0.05 and each dime is worth $0.10. The total amount is $1.70, so $0.05n + 0.10d = 1.70$. Substituting $d = n + 2$ into the equation gives $0.05n + 0.10(n + 2) = 1.70$. Solving this equation for $n$ gives $n = 10$, meaning she has 10 nickels.

Question 14

Solve the problem.
-A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has 10 more of the twenties. The total value of the money is $\$ 825$. Find the number of five-dollar bills that the teller has.

Accepted Answer

Let the number of five-dollar bills be $ x $. Then the number of twenty-dollar bills is $ x + 10 $. The total value equation is $ 5x + 20(x + 10) = 825 $. Solving this gives $ x = 25 $.

Question 15

Solve the problem.
-A cashier has a total of 136 bills, made up of fives and tens. The total value of the money is $\$ 930$. How many ten-dollar bills does the cashier have?

Accepted Answer

The problem can be solved using a system of equations. Let $x$ be the number of ten-dollar bills and $y$ be the number of five-dollar bills. We have two equations: $x + y = 136$ (total number of bills) and $10x + 5y = 930$ (total value of the bills). Solving these equations simultaneously, we find that $x = 50$, meaning the cashier has 50 ten-dollar bills.

Question 16

Solve the problem.
-There were 540 people at a play. The admission price was $\$ 2.00$ for adults and $\$ 1.00$ for children. The admission receipts were $\$ 890$. How many adults and children attended?

Accepted Answer

Let $x$ be the number of adults and $y$ be the number of children.We have the system of equations:$$x + y = 540$$$$2x + y = 890$$Solving the system of equations, we get:$$x = 350$$$$y = 190$$Therefore, there were 350 adults and 190 children at the play.

Question 17

Solve the problem.
-There were 35,000 people at a ball game in Los Angeles. The day's receipts were $\$ 253,000$. How many people paid $\$ 11.00$ for reserved seats and how many paid $\$ 5.00$ for general admission?

Accepted Answer

Let the number of people who paid $11 be x and those who paid $5 be y. We have two equations: x + y = 35,000 (total number of people) and 11x + 5y = 253,000 (total receipts). Solving these equations simultaneously gives x = 13,000 and y = 22,000.

Question 18

Solve the problem.
-Bert is 27.5 kilometers away from Brenda. Both begin to walk toward each other at the same time. Bert walks at 3.5 kilometers per hour. They meet in 5 hours. How fast is Brenda walking?

Accepted Answer

Brenda is walking at 2 kilometers per hour. In 5 hours, Bert covers 17.5 kilometers (3.5 km/h * 5 h), leaving 10 kilometers (27.5 km - 17.5 km) for Brenda, who covers this distance in 5 hours, resulting in a speed of 2 km/h (10 km / 5 h).

Question 19

Solve the problem.
-Candy and Delvis are riding bicycles in the same direction. Candy is traveling at a speed of 8 miles per hour, and Delvis is traveling at a speed of 5 miles per hour. In 5 hours what is the distance between them (assuming that they began at the same point and time)?

Accepted Answer

The answer of Solve the problem.
-Candy and Delvis are riding...

Question 20

Solve the problem.
-From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 14 miles per hour. In how many hours will they be 92 miles apart?

Accepted Answer

The answer of Solve the problem.
-From a point on a...

Quiz 2: Linear Equations, Inequalities, and Applications

Solve the percent problem. -After receiving a discount of $13.5 \%$ on its bulk order of typewriter ribbons, John's Office Supply pays $\$ 6920$ . What was the price of the order before the discount?

Solve the percent problem. -After spending $\$ 3650$ for tables and $\$ 3250$ for chairs, a convention center manager finds that $15 \%$ of his original budget remains. Find the amount that remains. Round your answer to the nearest dollar, if necessary.

Solve the percent problem. -Midtown Antiques collects $6 \%$ sales tax on all sales. If total sales including tax are $\$ 1754.33$ , find the portion that is the tax. Round your answer to the nearest cent.

Solve the investment problem. -Mardi received an inheritance of $\$ 40,000$ . She invested part at $12 \%$ and deposited the remainder in tax-free bonds at $7 \%$ . Her total annual income from the investments was $\$ 4300$ . Find the amount invested at $12 \%$ .

Solve the investment problem. -Walt made an extra $\$ 5000$ last year from a part-time job. He invested part of the money at $10 \%$ and the rest at $8 \%$ . He made a total of $\$ 420$ in interest. How much was invested at $8 \%$ ?

Solve the investment problem. -Roberto invested some money at $8 \%$ , and then invested $\$ 2000$ more than twice this amount at $10 \%$ . His total annual income from the two investments was $\$ 3560$ . How much was invested at $10 \%$ ?

Solve the investment problem. -A merchant has coffee worth $\$ 5$ a pound that she wishes to mix with 80 pounds of coffee worth $\$ 8$ a pound to get a mixture worth $\$ 7$ a pound. How many pounds of the $\$ 5$ coffee should be used?

Solve the problem. -Jay drove 268 kilometers at the average rate of 67 kilometers per hour. How long did the trip take?

Solve the problem. -Janet drove 360 kilometers and the trip took 5 hours. How fast was Janet traveling?

Solve the problem. -What amount of money is found in a coin purse containing 21 dimes and 15 quarters?

Solve the problem. -An equilateral triangle has perimeter 69 inches. What would be the perimeter of a square whose sides each measure the same length as the side of the triangle?

Solve the problem. -A convention manager finds that she has $\$ 1310$ , made up of twenties and fifties. She has a total of 43 bills. How many fifty-dollar bills does the manager have?

Solve the problem. -A woman has $\$ 1.70$ in dimes and nickels. She has 2 more dimes than nickels. How many nickels does she have?

Solve the problem. -A bank teller has some five-dollar bills and some twenty-dollar bills. The teller has 10 more of the twenties. The total value of the money is $\$ 825$ . Find the number of five-dollar bills that the teller has.

Solve the problem. -A cashier has a total of 136 bills, made up of fives and tens. The total value of the money is $\$ 930$ . How many ten-dollar bills does the cashier have?

Solve the problem. -There were 540 people at a play. The admission price was $\$ 2.00$ for adults and $\$ 1.00$ for children. The admission receipts were $\$ 890$ . How many adults and children attended?

Solve the problem. -There were 35,000 people at a ball game in Los Angeles. The day's receipts were $\$ 253,000$ . How many people paid $\$ 11.00$ for reserved seats and how many paid $\$ 5.00$ for general admission?

Solve the problem. -Bert is 27.5 kilometers away from Brenda. Both begin to walk toward each other at the same time. Bert walks at 3.5 kilometers per hour. They meet in 5 hours. How fast is Brenda walking?

Solve the problem. -Candy and Delvis are riding bicycles in the same direction. Candy is traveling at a speed of 8 miles per hour, and Delvis is traveling at a speed of 5 miles per hour. In 5 hours what is the distance between them (assuming that they began at the same point and time) ?

Solve the problem. -From a point on a river, two boats are driven in opposite directions, one at 9 miles per hour and the other at 14 miles per hour. In how many hours will they be 92 miles apart?

Quiz 2: Linear Equations, Inequalities, and Applications

Solve the percent problem. -After receiving a discount of 13.5%13.5 \%13.5% on its bulk order of typewriter ribbons, John's Office Supply pays $6920\$ 6920$6920 . What was the price of the order before the discount?

Solve the percent problem. -After spending $3650\$ 3650$3650 for tables and $3250\$ 3250$3250 for chairs, a convention center manager finds that 15%15 \%15% of his original budget remains. Find the amount that remains. Round your answer to the nearest dollar, if necessary.

Solve the percent problem. -Midtown Antiques collects 6%6 \%6% sales tax on all sales. If total sales including tax are $1754.33\$ 1754.33$1754.33 , find the portion that is the tax. Round your answer to the nearest cent.

Solve the investment problem. -Mardi received an inheritance of $40,000\$ 40,000$40,000 . She invested part at 12%12 \%12% and deposited the remainder in tax-free bonds at 7%7 \%7% . Her total annual income from the investments was $4300\$ 4300$4300 . Find the amount invested at 12%12 \%12% .

Solve the investment problem. -Walt made an extra $5000\$ 5000$5000 last year from a part-time job. He invested part of the money at 10%10 \%10% and the rest at 8%8 \%8% . He made a total of $420\$ 420$420 in interest. How much was invested at 8%8 \%8% ?

Solve the investment problem. -Roberto invested some money at 8%8 \%8% , and then invested $2000\$ 2000$2000 more than twice this amount at 10%10 \%10% . His total annual income from the two investments was $3560\$ 3560$3560 . How much was invested at 10%10 \%10% ?

Solve the investment problem. -A merchant has coffee worth $5\$ 5$5 a pound that she wishes to mix with 80 pounds of coffee worth $8\$ 8$8 a pound to get a mixture worth $7\$ 7$7 a pound. How many pounds of the $5\$ 5$5 coffee should be used?