Math 7 Unit 3 Percent Applications Review

John estimates that a piece of metal measures 7.5 cm. If it actually measures 7.68 cm, what is the percent error of John's estimate?

• 2.34%

• 2.38%

• 13%

• 48.83%

Answer explanation

Method 1 (photo left):

Set up a proportion. Since you are finding the percent, x goes over 100. The estimated length of 7.5 is the numerator. The actual length of 7.68 is the denominator. Then find the crossproducts, which are 7.68x and 750. Divide 750 by 7.68 which is 97.66% Then find the difference (100% - 97.66% = 2.38%), so the percent error is 2.34%.

Method 2 (photo right):

First subtract the estimated and actual values (7.68 - 7.5 = 0.18) to find the difference. Set up a proportion. since you are finding the percent, x goes over 100. The difference is the numerator and the actual length is the denominator. Then find the crossproducts, which are 7.68x and 18. Divide 18 by 7.68 which is 2.34, so the percent error is 2.34%.

Alternate Method:

Also, the percent error can be found by subtracting the estimated and actual values, then dividing it by the actual value, and multiplying by 100.

In this case, the percent error is 2.34%.

In Season 1, Jackson STRUCK OUT 25 times in 75 times at bat. In Season 2, he STRUCK OUT 35 times in 105 times at bat. In Season 3, Jackson STRUCK OUT 21 times in 120 times at bat. What percentage of times at bat did Jackson actually hit the ball?

Answer explanation

Find the number of hits for Jackson by subtracting the strike outs from the times at bat each season.

Season 1: 75 - 25 = 50 hits

Season 2: 105 - 35 = 70 hits

Season 3: 120 - 21 = 99 hits

Find the sum: 50 + 70 + 99 = 219 hits

Find the total number of times at bat for Jackson by adding: 75 + 105 + 120 = 300 times at bat.

Set up a proportion. Since you are finding the percent, x goes over 100. The part (or numerator) is 219. The whole (or denominator) is 300. Find the crossproducts, which are 300x and 21,900. Divide 21,900 by 300 to get 73. Jackson hit the ball 73% of the times he was at bat.

A boutique sells a handbag with a 90% markup. If the boutique sells the handbag for $209.00, what is their non-markup price?

• $90

• $110

• $150

• $200

Answer explanation

Method 1 (photo left):

To find the percent markup, add 100% (original) + 90% (new) = 190%.

Set up a proportion by placing 190 over 100. Then put the new price of 209 over w, which represents the original (whole). Find the crossproducts, which are 190w and 20900. Then divide 20900 by 190 to find w=110. The original price is $110.

Method 2 (photo right):

The non-markup price of the handbag is $110. This is calculated by dividing the selling price by 1.90 (190% = 1.90). The correct choice is $110.

April took out a $600 loan from the bank.

At the end of 4 years, she pays back the principal, plus $48 simple interest.

What was the percent of annual interest paid on this loan?

• 8%

• 6%

• 4%

• 2%

Answer explanation

To find the interest she paid each year, divide $48 by 4 = $12 per year. Set up a proportion placing x over 100 to find the percent of interest. Put the annual interest of $12 which is the part over the principal of $600, which is the whole. Find the crossproducts of 600x and 1200. Divide 1200 by 600 = 2. The annual interest rate is 2%.

Michael and Imani go out to eat for lunch.   

1) If their food and beverages cost $28.20 and there is an 7% meal tax, how much is the bill including tax? (Round your answer to the nearest cent.)

2) After adding a tip, the total lunch cost was $34.70. What percentage of the total bill including tax was the tip? (Round your answer to the nearest percent.)

• $28.20; 18%

• $30.17; 18%

• $28.20; 15%

• $30.17; 15%

Answer explanation

1) Find the meal tax

The meal tax is found by setting up a proportion with 7 over 100 and x over 28.20. The crossproudcts are 100x and 197.4. After dividing by 100, the tip is rounded to $1.97.

2) Find the bill total including tax

Add $1.97 to $28.20 to get the bill total of $30.17.

3) Find the tip amount

Subtract $34.70 - $30.17 = $4.53.

4) Find the tip percent

Set up a proportion by placing x over 100 and the tip of $4.53 over the bill with tax of $30.17. The crossproducts are 30.17x and 453. Divide by 30.17 and round the answer to 15%

The bill including tax is $30.17 and the tip is 15% of that bill.

**It is not customary to include the meal tax when figuring a tip, but that is what this question asks us to find.

Mike discovered that approximately 80% of his 40 classmates enjoy pop music. However, 68% of his 50 family members enjoy pop music. Do more classmates or family members enjoy pop music?

• The same number of classmates enjoy pop music as family members.

• More of his family members enjoy pop music than his classmates.

• More of his classmates enjoy pop music than his family members

• There is not enough information to determine the answer.

Answer explanation

Find 80% of 40 by multiplying 0.80 x 40 = 32, so 32 classmates enjoy pop music.

Find 68% of 50 by multiplying 0.68 x 50 = 34, so 34 family members enjoy pop music.

Therefore, more family members enjoy pop music than classmates.

During the first check-up at the vet, Bella's puppy weighed 800 grams. On the second check-up, the puppy had gained 300 grams. On the third check-up, the puppy had gained another 300 grams. What is the percent increase since the first check-up in the puppy's weight rounded to the nearest percent?

• 100% increase

• 75% increase

• 50% increase

• 25% increase

Answer explanation

First, find the total increase in the puppy's weight: 300 + 300 = 600

Then set up a proportion by placing x over 100 and 600 over 800. Find the crossproducts of 800x and 60000. Divide 60000 by 800 to get 75.

The puppy's weight increased by 75%.

Oliver purchases a book online that usually costs $49.99, but it was on sale for 20% off.

How much did Oliver pay? Round to the nearest cent.

• $19.99

• $29.99

• $30

• $39.99

Answer explanation

Method 1

Find the discount by multiplying 0.20 x 49.99 = 9.998 and rounding the answer to 10.00. Then subtract the discount from the original price, 49.99 - 10.00 = 39.99. So the book would cost Oliver $39.99.

Method 2

First, find the percent remaining by subtracting 20% from 100%. Multiply 0.80 x 49.99 = 39.992 and rounding the answer to 39.99. So the book would cost Oliver $39.99

Method 3

You could also set up and solve a proportion by placing 20 over 100 and x over 49.99. Then find the crossproducts of 100x and 999.8. Divide 999.8 by 100 to get 9.998. Round the number to 10.00. Subtract 10.00 from 49.99 to get 39.99. So that's $39.99.

Method 4

You could set up a different proportion by subtracting the discount percent of 20% from 100% to get 80%. Place 80 over 100 and x over 49.99. Find the crossproducts of 100x and 3999.2. Then divide 3999.2 by 100 to get 39.9992 which rounds to 39.99. So the book would cost $39.99.

John measures and finds that he can do a vertical jump that is 28% of his height. If John can jump 15.6 inches, how many inches tall is he? (Round your answers to the nearest inch)

Answer explanation

Method 1

Set up a proportion by placing 28 over 100 and 15.6 over x. Find the crossproducts of 28x and 1560. Divide 1560 by 28 = 55.714... Round the answers to the nearest inch, so x=56. The correct answer is 56 in.

Method 2

Use the percent equation to find the whole.

15.6 = 0.28w

Divided 15.6 by 0.28 = 55.714...

Round the answer to the nearest inch.

The correct answer is 56 in.

Emma climbed 330.3 meters up a hill. If she is 70% of the way up, how tall is the hill? (Round your answer to the nearest hundredth.)

• 231.21 meters

• 471.86 meters

• 476.77 meters

• 576.91 meters

Answer explanation

Method 1

Set up a proportion by placing 70 over 100 and 330.3 over x. Find the crossproducts of 70x and 33030. Divided 33030 by 70 = 471.857... Round to 471.86. The correct answer is 471.86 m.

Method 2

Use the percent equation to solve for the whole:

part = % x whole

303.3 = 0.70w

Divided 303.3 by 0.70 = 471.857...

Round to 471.86.

The correct answer is 471.86 m.