SAT MATH - PERCENT WORD PROBLEMS

Problem 1 :

There are n candies in a jar. If one candy is removed, what percent of the candies are left in terms of n?

(A)  100 (1 - n)%

(B)  100(¹⁄n - 1)

(C)  100 (n - ¹⁄n)%

(D)  100⁽ⁿ ⁻ ¹⁾⁄n%

Solution :

There are n candies in a jar, if one candy is removed, n - 1 candies are left in the jar.

Percent of the candies left in the jar :

= 100⁽ⁿ ⁻ ¹⁾⁄n%

Therefore, the correct answer is option (D).

Problem 2 :

The price of a cellphone was discounted by 25% and then discounted an additional 20%, to become $348. What was the original price of the cellphone before it was discounted twice?

(A)  $580

(B)  $620

(C)  $650

(D)  $680

Solution :

Let x be the original price of the cellphone.

After 25% discount, the price of the cellphone :

= (100 - 25)% of x

= 75% of x

= 0.75x

After additional 20% discount, the price of the cellphone :

= (100 - 20)% of 0.75x

= 80% of 0.75x

= 0.8(0.75)x

= 0.6x

Given : After 25% and 20% discounts, the price of the cellphone is $348.

0.6x = 348

Divide both sides by 0.6.

x = 580

The original price of the cellphone was $580.

Therefore, the correct answer is option (A).

Problem 3 :

How many milliliters of 65% acid solution must be added to 60 milliliters of a 40% acid solution in order to make a 50% acid solution?

Solution :

Let x be the amount of 65% acid solution to be added.

Amount of acid in x milliliters of 65% acid solution :

= 65% of x

= 0.65x

Amount of acid in 60 milliliters of 40% acid solution :

= 40% of 60

= 0.4(60)

= 24

After adding x milliliters of 65% acid solution to 60 milliliters of 40% acid solution, amount of acid in the resultant solution :

= 0.65x + 24

Given : The resultion solution has 50% acid.

0.65x + 24 = 50% of (x + 60)

0.65x + 24 = 0.5(x + 60)

0.65x + 24 = 0.5x + 30

0.15x = 6

x = 40

Therefore, 40 milliliters of 65% acid solution must be added.

Problem 4 :

Bob invested $7,500 in stocks and bonds. The stocks pay 6.5% interest a year and the bonds pay 8% interest a year. His interest income is $528 this year. How much
money was invested in stocks?

Solution :

Let x be the amount invested in stocks.

Then the amount invested in bonds is (7500 - x).

Interest from stocks + interest from bonds = total interest income

0.065x + 0.08(7500 - x) = 528

0.065x + 600 - 0.08x = 528

600 - 0.015x = 528

- 0.015x = -72

x = 4800

Therefore, $4,800 was invested in stocks.

Problem 5 :

The sale price of a laptop is $505.44 after 35% discount and 8% additional tax. What was the original price of the laptop before discount and tax? (calculator)

Solution :

Let x be the original price of the laptop.

After 35% discount, the price of the laptop :

= (100 - 35)% of x

= 65% of x

= 0.65x

After 35% additional tax, the price of the cellphone :

= (100 + 8)% of 0.65x

= 108% of 0.65x

= 1.08(0.65x)

= 0.702x

Given : The sale price of a laptop is $505.44 after 35% discount and 8% additional tax.

0.702x = 505.44

x = 720

Therefore, the original price of the laptop was $720.

Problem 6 :

A chemist mixes a 40% acid solution and a 30% acid solution. How many liters of the 40% solution must be added to produce 50 liters of a solution that is 36% acid?

(A)  24

(B)  26

(C)  30

(D)  32

Solution :

Given : Number of liters in the final solution is 50.

Let x be the number of liters of 40% acid solution to be added.

Then the amount of 30% acid solution is (50 - x) liters.

Amount of acid in x liters of 40% acid solution :

= 40% of x

= 0.4x

Amount of acid in (50 - x) liters of 30% acid solution :

= 30% of (50 - x)

= 0.3(50 - x)

= 15 - 0.3x

After mixing 40% acid solution and 30% acid solution, amount of acid in the resultant solution :

= 0.4x + (15 - 0.3x)

= 0.4x + 15 - 0.3x

= 0.1x + 15

Given : The resultant solution 50 liters has 36% acid.

0.1x + 15 = 36% of 50

0.1x + 15 = 0.36(50)

0.1x + 15 = 18

0.1x = 3

x = 30

30 liters of 40% acid solution should be added.

Therefore, the correct answer is option (C).

Problem 7 :

Victor invests part of his $5,000 in a savings account that pays 4.5% annual simple interest. He invests the rest in bonds that pay 8% annual simple interest. Let s be the amount invested in savings and r be the amount invested in bonds. Victor’s total income in one year from these investments is $305.50. Which of the following  systems of equations represents this relationship?

Solution :

s ----> amount invested in savings

r -----> amount invested in bonds

Given : The toal investment is $5000.

s + r = 5000

Given : Savings account pays 4.5% annual simple interest.

= 4.5% of s

= 0.045s

Given : Bonds pay 8% annual simple interest

= 8% of

= 0.08r

Total interest earned = 0.045s + 0.08r

Given : Total income in one year from these investments is $305.50.

0.045s + 0.08r = 305.50

System of equations systems of equations represents the given relationship :

s + r = 5000

0.045s + 0.08r = 305.50

Therefore, the correct answer is option (C).

Problem 8 :

A sporting goods store added 50% profit cost and 8% tax to the price of a backpack, which then became $129.60. What was the price of the backpack before adding profit and tax?

Solution :

Let x be the price of the backpack before adding profit and tax.

After 50% profit, the price of the backpack would be

= (100 + 50)% of x

= 150% of x

= 1.5x

After 8% tax, the price of the backpack would be

= (100 + 8)% of 1.5x

= 108% of 1.5x

= 1.08(1.5x)

= 1.62x

Given : After 50% profit cost and 8% tax, the price of a backpac was $129.60.

1.62x = 129.60

x = 80

Therefore, the price of the backpack before adding profit and tax was $80.

Problem 9 :

There are 800 students in a school and 45% of the students are male. If 30% of the male students and 25% of the female students play varsity sports, how many students play varsity sports?

Solution :

Number of male students :

= 45% of 800

= 0.45(800)

= 360

Number of female students :

= 800 - 360

= 440

Given : 30% of the male students and 25% of the female students play varsity sports.

30% of the male students :

= 30% 360

= 0.3(360)

= 108

25% of the female students :

= 25% 440

= 0.25(440)

= 110

The number of students who play varsity sports :

= 108 + 110

= 218

Problem 10 :

A sudent scored 45% of the total marks in an exam and got failed by 45 marks. If the pass mark is 450, find the total marks in the exam.

Solution :

Let x be the total marks in the exam.

Marks scored by the student :

= 45% of x

= 0.45x

Given : The student scored 45% of the total marks and got failed by 45 marks.

If he had scored 45 more marks, he would have passed the examination.That is, he would have received the pass mark 450.

0.45x + 45 = 450

0.45x = 405

x = 900

Therefore, the total marks in the exam is 900.

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