SOLVING MULTI STEP WORD PROBLEMS INVOLVING PERCENTAGE

Problem 1 :

Sam opened a money-market account that pays 3% simple interest. He started the account with $7,000 and made no further deposits. When he closed the account, he had earned $1,050 in interest. How long did he keep his account open?

Solution :

Principal amount (P) = 7000

Tate of interest (R) = 3% and interest (I) = 1050

Number of years = ?

Using simple interest formula

I = PNR/100

1050 = (7000 ⋅ N ⋅ 3)/100

1050/(70⋅3) = N

N = 5 years

Problem 2 :

Amy bought a box of chocolates originally priced at $14. She received a 15% discount on the original price, and then she paid a 4% sales tax on the purchase price. What is the total amount that Amy paid for the box of chocolates?

Solution :

Original price = $14

Amount that she has to pay after the discount

= (100 - 15)% of the original price

= 85% of 14

= 0.85 x 14

= $11.9

As sales tax, she has to pay 4%.

Total amount after the sales tax = (100 + 4)% of 11.9

= 114 % of 11.9

= 1.14 x 11.9

= $13.56

So, she has to pay $13.56 for a box of chocolate.

Problem 3 :

Maria works for an automobile dealership. She earns a 10% commission on each motorcycle she sells and a 15% commission on each car she sells. Maria sells a motorcycle for $5,000 and a car for $25,000. What is the total commission that she will earn on the sale of these two vehicles?

Solution :

Commission amount for motorcycle = 10%

Commission amount for car = 15%

Selling price of motorcycle = $5000

Selling price of car = $25000

10% of 5000 + 15% of 25000

= 0.10(5000) + 0.15(25000)

= 500 + 3750

= $4250

Problem 4 :

A pair of shoes usually sells for $69. If the shoes are 30% off, and sales tax is 6%, what is the total price of the shoes including tax?

Solution :

Selling price of shoe = $69

Offer price = (100 - 30) % of 69

= 70% of 69

= 0.70(69)

= $48.3

Sales tax = (100 + 6)% of 48.3

= 106% of 48.3

= 1.06 (48.3)

= $51.198

Problem 5 :

Martha estimated there were 87 marbles in a jar for a contest. The actual number of marbles in the jar was 109. What was the percent error of Martha's estimation?

Solution :

Number of marbles she has estimated = 87

Actual number of marbles = 109

Difference = 109 - 87

= 22

Percentage error = (22 / 87) x 100%

= 0.25 x 100%

= 25%

So, the percentage error is 25%.

Problem 6 :

Tessa bought stock in a restaurant for $170.00. Her stock is now worth $251.60. What is the percentage increase of the value of Tessa's stock?

Solution :

Value of stock = $170

New worth = 251.60

Percentage increase or decrease

= [(new value - old value) / old value] x 100%

=  [(251.60 - 170)/170] x 100%

= (81.6/170) x 100%

= 0.48 x 100%

= 48%

Problem 7 :

Jane moved from a house with 61 square feet of closet space to an apartment with 36.6 square feet of closet space. What is the percentage decrease of Jane's closet space?

Solution :

Old area = 61 square feet

New area = 36.6 square feet

Percentage decrease = [(old area - new area) / old area] x 100%

= [ (61 - 36.6) / 36.6 ] x 100%

= (24.4/36.6) x 100%

= 0.666 x 100%

= 66.6% 

Problem 8 :

A zookeeper predicted the weight of a new baby elephant to be 265 pounds when it was born. The elephant actually weighed 297 pounds at birth. What was the percent error of the zookeeper's prediction?

Solution :

Percentage error = [(old value - new vale) / old value] x 100%

= [(297 - 265) / 265] x 100%

= (32/265) x 100%

= 0.12 x 100%

= 12%

So, the required percentage error is 12%.

Problem 9 :

Jason and his friend went to a restaurant for dinner. The food that they ordered cost $25. A 7% sales tax was applied to the total. After the sales tax was applied, Jason paid a 15% tip on the total bill. How much did Jason pay at the restaurant?

Solution :

Cost of food = $25

Sales tax = 7%

Amount to be paid after sales = 107% of 25

= 1.07 x 25

= $26.75

Tip = 15%

Amount to be paid after tip = 105% of 26.75

= 1.05 x 26.75

= $28.08