Question 1

Solve the problem.
-Devon purchased tickets to an air show for 6 adults and 2 children. The total cost was $114. The cost of a child's ticket was $7 less than the cost of an adult's ticket. Find the price of an adult's ticket
And a child's ticket.

Accepted Answer

Let the cost of an adult's ticket be x. Then the cost of a child's ticket is x - 7. The equation is 6x + 2(x - 7) = 114. Solving gives x = 16, so the adult's ticket is $16 and the child's ticket is $9.

Question 2

Graph the set of numbers given in interval notation. Then write an inequality statement in x describing the numbers
graphed.
-$[2, \infty)$

Accepted Answer

The answer of Graph the set of numbers given in...

Question 3

Solve.
-If $26,000 is invested at 10% simple annual interest, how much should be invested at 12% annual simple interest so that the total yearly income from both investments is $5000?

Accepted Answer

The answer of Solve.
-If $26,000 is invested at 10% simple...

Question 4

Solve the problem.
-A convenience store employee is counting $10 and $20 bills. If there are six times as many $10 bills as $20 bills and the total amount is $1920, find the number of each type of bill.

Accepted Answer

Let the number of $20 bills be x. Then, the number of $10 bills is 6x. The total value is $20x + $10(6x) = $1920. Solving this equation gives x = 24 for the $20 bills and 6x = 144 for the $10 bills.

Question 5

Solve.
-Jeff starts driving at 65 miles per hour from the same point that Lauren starts driving at 40 miles per hour. They drive in opposite directions, and Lauren has a half-hour head start. How long will they Be able to talk on their cell phones that have a 330-mile range?

Accepted Answer

The answer of Solve.
-Jeff starts driving at 65 miles per...

Question 6

Graph the set of numbers given in interval notation. Then write an inequality statement in x describing the numbers
graphed.
-$(-\infty,-5]$

Accepted Answer

The answer of Graph the set of numbers given in...

Question 7

Solve.
-A motorcycle traveling at 50 miles per hour overtakes a car traveling at 30 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles?

Accepted Answer

The car travels 30 miles per hour for 3 hours, covering 90 miles. The motorcycle catches up at a relative speed of 20 miles per hour (50 - 30). It takes 4.5 hours to close the 90-mile gap, so the distance from the start is 50 mph * 4.5 hours = 225 miles.

Question 8

Solve.
-Dave can hike on level ground 3 miles an hour faster than he can on uphill terrain. Yesterday, he hiked 32 miles, spending 2 hours on level ground and 5 hours on uphill terrain. Find his average
Speed on level ground.

Accepted Answer

Dave's speed on level ground is $6 \frac { 5 } { 7 } \mathrm { mph }$ after setting up and solving the equation based on the given information.

Question 9

Solve the problem.
-On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of bracelets at $4 each and a number of necklaces at $13 each. She wrote a check for $930 to pay for the order. How many bracelets and how many necklaces did Rosaria purchase?

Accepted Answer

Let x be the number of bracelets and y be the number of necklaces. We have two equations: x + y = 120 and 4x + 13y = 930. Solving these equations, we find x = 70 and y = 50.

Question 10

Solve.
-Alexander and Judy are 32 miles apart on a calm lake paddling toward each other. Alexander paddles at 5 miles per hour, while Judy paddles at 8 miles per hour. How long will it take them to
Meet?

Accepted Answer

The answer of Solve.
-Alexander and Judy are 32 miles apart...

Question 11

Solve.
-On a road trip, five friends drove at 50 miles per hour to California. On the way home, they took the same route but drove 75 miles per hour. How many miles did they drive on the way to California if the round trip took 10 hours?

Accepted Answer

The total distance for the round trip is the sum of the distance to California and the distance back. Let $ x $ be the distance to California. The time to California is $ \frac{x}{50} $ hours, and the time back is $ \frac{x}{75} $ hours. The total time is $ \frac{x}{50} + \frac{x}{75} = 10 $ hours. To find $ x $, solve the equation: $ \frac{x}{50} + \frac{x}{75} = 10 $. Finding a common denominator (150) and solving for $ x $ gives $ x = 300 $ miles.

Question 12

Solve.
-How can $42,000 be invested, part at 4% annual simple interest and the remainder at 10% annual simple interest, so that the interest earned by the two accounts is equal at the end of the year?

Accepted Answer

Let the amount invested at 4% be $x. Then, the amount invested at 10% is $42,000 - $x. The interest from the first investment is 0.04x, and from the second investment is 0.10(42,000 - x). Setting these equal to each other because the interests are equal: 0.04x = 0.10(42,000 - x). Solving this equation gives x = $30,000 at 4%, and thus $12,000 at 10%.

Question 13

Solve the problem.
-Jon throws all his nickels and dimes in a jar at home each day. He counted all his coins one day and found that he had collected $37.45. If there were five times as many nickels as dimes, how many of Each coin does he have?

Accepted Answer

Let the number of dimes be x and the number of nickels be 5x. The value of the dimes is 0.10x and the value of the nickels is 0.05(5x) = 0.25x. The total value is 0.10x + 0.25x = 0.35x = $37.45. Solving for x gives x = 107, so there are 107 dimes and 5*107 = 535 nickels.

Question 14

Graph the set of numbers given in interval notation. Then write an inequality statement in x describing the numbers
graphed.
-$( - \infty , 2 )$

Accepted Answer

The answer of Graph the set of numbers given in...

Question 15

Graph the set of numbers given in interval notation. Then write an inequality statement in x describing the numbers
graphed.
-$(4, \infty)$

Accepted Answer

The answer of Graph the set of numbers given in...

Question 16

Solve.
-Melissa invested a sum of money at 3% annual simple interest. She invested three times that sum at 5% annual simple interest. If her total yearly interest from both investments was $3600, how much
Was invested at 3%?

Accepted Answer

The answer of Solve.
-Melissa invested a sum of money at...

Question 17

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-The radiator in a certain make of car needs to contain 20 liters of 40% antifreeze. The radiator now contains 20 liters of 20% antifreeze. How many liters of this solution must be drained and replaced
With 100% antifreeze to get the desired strength?

Accepted Answer

The answer of Solve. If needed, round money amounts to...

Question 18

Solve the problem.
-Sue took her collection of nickels and dimes to deposit in the bank. She has five fewer nickels than dimes. Her total deposit was $45.35. How many dimes did she deposit?

Accepted Answer

Let the number of dimes be $d$ and the number of nickels be $n$. The problem states that Sue has five fewer nickels than dimes, so $n = d - 5$. The total value of the coins is $45.35, or 4535 cents. Since dimes are worth 10 cents and nickels are worth 5 cents, the total value can be represented as $10d + 5n = 4535$. Substituting $n = d - 5$ into the equation gives $10d + 5(d - 5) = 4535$, which simplifies to $15d - 25 = 4535$. Solving for $d$ gives $d = 304$, so Sue deposited 304 dimes.

Question 19

Solve.
-Linda and Dave leave simultaneously from the same starting point biking in opposite directions. Linda bikes at 5 miles per hour and Dave bikes at 9 miles per hour. How long will it be until they
Are 30 miles apart from each other?

Accepted Answer

Since Linda and Dave are biking away from each other, their speeds add up. Together, they cover $5 + 9 = 14$ miles per hour. To find out how long it takes for them to be 30 miles apart, divide the distance by their combined speed: $30 \div 14 = 2 \frac{1}{7}$ hours.

Question 20

Solve.
-Kevin invested part of his $10,000 bonus in a certificate of deposit that paid 6% annual simple interest, and the remainder in a mutual fund that paid 11% annual simple interest. If his total Interest for that year was $900, how much did Kevin invest in the mutual fund?

Accepted Answer

Let x be the amount invested in the mutual fund. Then, $10,000 - x is the amount invested in the certificate of deposit. The total interest is given by 0.06($10,000 - x) + 0.11x = $900. Solving this equation, we find x = $6000.

Quiz 2: Equations, Inequalities, and Problem Solving

Solve the problem. -Devon purchased tickets to an air show for 6 adults and 2 children. The total cost was $114. The cost of a child's ticket was $7 less than the cost of an adult's ticket. Find the price of an adult's ticket And a child's ticket.

Graph the set of numbers given in interval notation. Then write an inequality statement in x describing the numbers graphed. - [2,∞) [2, \infty) [2,∞)

Solve. -If $26,000 is invested at 10% simple annual interest, how much should be invested at 12% annual simple interest so that the total yearly income from both investments is $5000?

Solve the problem. -A convenience store employee is counting $10 and $20 bills. If there are six times as many $10 bills as $20 bills and the total amount is $1920, find the number of each type of bill.

Solve. -Jeff starts driving at 65 miles per hour from the same point that Lauren starts driving at 40 miles per hour. They drive in opposite directions, and Lauren has a half-hour head start. How long will they Be able to talk on their cell phones that have a 330-mile range?

Graph the set of numbers given in interval notation. Then write an inequality statement in x describing the numbers graphed. - (−∞,−5](-\infty,-5](−∞,−5]

Solve. -A motorcycle traveling at 50 miles per hour overtakes a car traveling at 30 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles?

Solve. -Dave can hike on level ground 3 miles an hour faster than he can on uphill terrain. Yesterday, he hiked 32 miles, spending 2 hours on level ground and 5 hours on uphill terrain. Find his average Speed on level ground.

Solve the problem. -On a buying trip in Los Angeles, Rosaria Perez ordered 120 pieces of jewelry: a number of bracelets at $4 each and a number of necklaces at $13 each. She wrote a check for $930 to pay for the order. How many bracelets and how many necklaces did Rosaria purchase?

Solve. -Alexander and Judy are 32 miles apart on a calm lake paddling toward each other. Alexander paddles at 5 miles per hour, while Judy paddles at 8 miles per hour. How long will it take them to Meet?

Solve. -On a road trip, five friends drove at 50 miles per hour to California. On the way home, they took the same route but drove 75 miles per hour. How many miles did they drive on the way to California if the round trip took 10 hours?

Solve. -How can $42,000 be invested, part at 4% annual simple interest and the remainder at 10% annual simple interest, so that the interest earned by the two accounts is equal at the end of the year?

Solve the problem. -Jon throws all his nickels and dimes in a jar at home each day. He counted all his coins one day and found that he had collected $37.45. If there were five times as many nickels as dimes, how many of Each coin does he have?

Graph the set of numbers given in interval notation. Then write an inequality statement in x describing the numbers graphed. - (−∞,2) ( - \infty , 2 ) (−∞,2)

Graph the set of numbers given in interval notation. Then write an inequality statement in x describing the numbers graphed. - (4,∞) (4, \infty) (4,∞)

Solve. -Melissa invested a sum of money at 3% annual simple interest. She invested three times that sum at 5% annual simple interest. If her total yearly interest from both investments was $3600, how much Was invested at 3%?

Solve the problem. -Sue took her collection of nickels and dimes to deposit in the bank. She has five fewer nickels than dimes. Her total deposit was $45.35. How many dimes did she deposit?

Solve. -Linda and Dave leave simultaneously from the same starting point biking in opposite directions. Linda bikes at 5 miles per hour and Dave bikes at 9 miles per hour. How long will it be until they Are 30 miles apart from each other?

Solve. -Kevin invested part of his $10,000 bonus in a certificate of deposit that paid 6% annual simple interest, and the remainder in a mutual fund that paid 11% annual simple interest. If his total Interest for that year was $900, how much did Kevin invest in the mutual fund?