Question 1

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-The number of video stores in a region recently decreased from 88 to 57. Find the percent of decrease.

Accepted Answer

The percent decrease is found by dividing the decrease in number by the original number, then multiplying by 100. So, $\frac{88 - 57}{88} \times 100 = 35.2\%$.

Question 2

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-A store is advertising 15% off sale on everything in the store. Find the discount of a fax machine that regularly sells for $150.

Accepted Answer

The discount is calculated as 15% of $150, which is $150 * 0.15 = $22.50.

Question 3

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-5% of students at a university attended a lecture. If 6000 students are enrolled at the university, about how many students attended the lecture?

Accepted Answer

5% of 6000 is calculated as (5/100) * 6000 = 300 students.

Question 4

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-A store is advertising 35% off sale on everything in the store. Find the sale price of a watch that regularly sells for $260.

Accepted Answer

The sale price of the watch is found by subtracting 35% of its original price from its original price. 35% of $260 is $91 (0.35 * $260 = $91). Subtracting this from the original price, $260 - $91 = $169.

Question 5

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-Ming got a 17% raise in her salary from last year. This year she is earning $119,340. How much did she make last year?

Accepted Answer

Ming's current salary is the result of a 17% raise from last year. To find her salary last year, divide her current salary by 1.17 (100% + 17% = 117% or 1.17 in decimal form). $119,340 / 1.17 = $102,000.

Question 6

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-Students at Maple School earned $636 selling candles. They want to accumulate $2000 for a club trip. What percent of their goal has been reached?

Accepted Answer

To find the percentage of the goal reached, divide the amount earned ($636) by the total goal ($2000) and multiply by 100. $ \frac{636}{2000} \times 100 = 31.8\% $.

Question 7

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-A store is advertising 35% off sale on everything in the store. Find the discount of a painting that regularly sells for $2900.

Accepted Answer

The discount is calculated as 35% of $2900, which is $2900 * 0.35 = $1015.00.

Question 8

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-Due to a lack of funding, the number of students enrolled at City College went from 6000 last year to 2000 this year. Find the percent of decrease in enrollment.

Accepted Answer

The percent decrease in enrollment is calculated by the formula: [(Old Value - New Value) / Old Value] * 100. Here, it is [(6000 - 2000) / 6000] * 100 = 66.7%.

Question 9

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-At a gourmet nut shop, nuts are sold in bulk. Cashews sell for $1.50 per pound and macadamia nuts sell for $8.50 per pound. Lee wishes to purchase 5 pounds of mixed nuts by mixing 3.5 pounds
Of cashews and 1.5 pounds of macadamia nuts. What will be the price per pound of the mixture?

Accepted Answer

The total cost of the cashews is 3.5 pounds * $1.50 = $5.25. The total cost of the macadamia nuts is 1.5 pounds * $8.50 = $12.75. The total cost of the mixture is $5.25 + $12.75 = $18.00. The mixture weighs 5 pounds, so the price per pound is $18.00 / 5 = $3.60.

Question 10

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-An automobile dealership recently reduced the price of a used sports car by 14%. If the price of the car was $25,600.00, find the sale price.

Accepted Answer

The sale price after a 14% reduction is found by calculating 86% (100% - 14%) of the original price: $25,600 * 0.86 = $22,016.00.

Question 11

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-The population of a town is currently 45,000. This represents an increase of 60% from the population 5 years ago. Find the population of the town 5 years ago. Round to the nearest whole
Number if necessary.

Accepted Answer

To find the population 5 years ago, let the original population be x. The population increased by 60%, so x + 0.60x = 45,000. Solving for x gives x = 45,000 / 1.60 = 28,125.

Question 12

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-Because of budget cutbacks, MaryAnn was required to take a 7% pay cut. If she earned $63,000 before the pay cut, find her salary after the pay cut.

Accepted Answer

MaryAnn's salary after a 7% pay cut is calculated by subtracting 7% of $63,000 from $63,000. 7% of $63,000 is $4,410, so her new salary is $63,000 - $4,410 = $58,590.

Question 13

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-The local clothing store marks up the price that it pays to the clothing manufacturer by 36%. If the selling price of a pair of jeans is $113, how much did the clothing store pay for the jeans?

Accepted Answer

The store marks up the price by 36%, meaning the selling price is 136% of the cost price. To find the cost price, divide the selling price by 1.36. $113 / 1.36 = $83.09.

Question 14

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-Jeans are on sale at the local department store for 25% off. If the jeans originally cost $59, find the sale price.

Accepted Answer

The sale price is found by subtracting 25% of the original price from the original price. 25% of $59 is $14.75. So, the sale price is $59 - $14.75 = $44.25.

Question 15

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-A company increased the number of its employees from 540 to 565 . What was the percent of increase in employees?

Accepted Answer

The percent of increase is calculated as the difference between the new and old values divided by the old value, multiplied by 100. In this case, the percent of increase is (565 - 540) / 540 * 100 = 4.6%.

Question 16

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-The owners of a candy store want to sell, for $6 per pound, a mixture of chocolate-covered raisins, which usually sells for $3 per pound, and chocolate-covered macadamia nuts, which usually sells
For $8 per pound. They have a 40-pound barrel of the raisins. How many pounds of the nuts should
They mix with the barrel of raisins so that they hit their target value of $6 per pound for the
Mixture?

Accepted Answer

To find the number of pounds of nuts needed, set up the equation: (3 * 40 + 8 * x) / (40 + x) = 6. Solving for x gives x = 60 lb.

Question 17

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-A chemist needs 170 milliliters of a 71% solution but has only 47% and 98% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Accepted Answer

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

Question 18

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-A store is advertising a 41% off sale on all new DVD releases. Find the sale price of a newly released DVD collectors set that regularly sells for $92.00.

Accepted Answer

The sale price can be found by subtracting the discount from the original price. The discount is 41% of $92.00, which is $37.72. So, the sale price is $92.00 - $37.72 = $54.28.

Question 19

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-The manager of a coffee shop has one type of coffee that sells for $7 per pound and another type that sells for $14 per pound. The manager wishes to mix 60 pounds of the $14 coffee to get a
Mixture that will sell for $13 per pound. How many pounds of the $7 coffee should be used?

Accepted Answer

To find the amount of $7 coffee needed, set up the equation: (7x + 14*60) / (x + 60) = 13. Solving for x gives x = 10 pounds.

Question 20

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place.
-How much pure acid should be mixed with 3 gallons of a 50% acid solution in order to get an 80% acid solution?

Accepted Answer

To achieve an 80% acid solution by mixing pure acid (100%) with a 3-gallon 50% acid solution, we set up the equation: 100%x + 50%(3) = 80%(x + 3). Solving for x gives x = 4.5 gallons.

Quiz 2: Equations, Inequalities, and Problem Solving

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -The number of video stores in a region recently decreased from 88 to 57. Find the percent of decrease.

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -A store is advertising 15% off sale on everything in the store. Find the discount of a fax machine that regularly sells for $150.

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -5% of students at a university attended a lecture. If 6000 students are enrolled at the university, about how many students attended the lecture?

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -A store is advertising 35% off sale on everything in the store. Find the sale price of a watch that regularly sells for $260.

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -Ming got a 17% raise in her salary from last year. This year she is earning $119,340. How much did she make last year?

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -Students at Maple School earned $636 selling candles. They want to accumulate $2000 for a club trip. What percent of their goal has been reached?

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -A store is advertising 35% off sale on everything in the store. Find the discount of a painting that regularly sells for $2900.

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -Due to a lack of funding, the number of students enrolled at City College went from 6000 last year to 2000 this year. Find the percent of decrease in enrollment.

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -An automobile dealership recently reduced the price of a used sports car by 14%. If the price of the car was $25,600.00, find the sale price.

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -Because of budget cutbacks, MaryAnn was required to take a 7% pay cut. If she earned $63,000 before the pay cut, find her salary after the pay cut.

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -The local clothing store marks up the price that it pays to the clothing manufacturer by 36%. If the selling price of a pair of jeans is $113, how much did the clothing store pay for the jeans?

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -Jeans are on sale at the local department store for 25% off. If the jeans originally cost $59, find the sale price.

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -A company increased the number of its employees from 540 to 565 . What was the percent of increase in employees?

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -A chemist needs 170 milliliters of a 71% solution but has only 47% and 98% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -A store is advertising a 41% off sale on all new DVD releases. Find the sale price of a newly released DVD collectors set that regularly sells for $92.00.

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. -How much pure acid should be mixed with 3 gallons of a 50% acid solution in order to get an 80% acid solution?