WORD PROBLEMS ON COINS ON SAT

Problem 1 :

Marie has $2.20 in dimes and quarters. If the number of dimes is 1/4 the number of quarters, how many dimes does she have?

A) 2    B) 4     C) 6     D) 8      E) 10

Solution :

Let n be number of quarters.

Number of dimes = (1/4)n ==> n/4

1 quarter = $0.25

1 dime= $0.10

0.25n + 0.10(n/4) = 2.20

(n + 0.10n)/4 = 2.20

1.10n = 8.8

n = 8.8/1.1

n = 8 (number of quarters)

Number of dimes = 8/4 ==> 2

Problem 2 :

Lisa has 45 coins that are worth a total of $3.50, if the coins are all nickels and dimes, how many more dimes than nickels does she have?

A) 5     B) 10      C) 15      D) 20        E) 25

Solution :

Let n = number of dimes

45 - n = number of nickel

0.10n + 0.05(45 - n) = 3.50

0.10n + 2.25 - 0.05n = 3.50

0.05n = 3.50 - 2.25

0.05n = 1.25

n = 1.25/0.05

n = 25

Number of dimes = 25

Number of nickels = 45 - 25 = 20

Difference between dimes and nickels = 25 - 20

= 5

So, she has 5 more dimes than nickels. Option (A) is correct.

Problem 3 :

A postal clerk sold 40 stamps for $5.40. Some were 10 cents stamps and some were 15 cent stamps. How many 10 cents stamps were there?

A) 10           B) 12         C) 20         D) 24        E) 28

Solution :

Let x = number of 10 cent stamps

40 - x = number of 15 cent stamps

0.10x = value of 10 cent stamps

0.10x + 0.15(40 - x) = 5.40

0.10x + 6 - 0.15x = 5.40

0.05x = 6 - 5.40

0.05x = 0.6

x = 0.6/0.05

x = 12

So, option (B) is correct.

Problem 4 :

Each of the 30 students in Homeroom 704 contributed either a nickel or a quarter to the Cancer Fund. If the total amount collected was $4.70. How many students contributed a nickel?

A) 10      B) 12       C) 14      D) 16      E) 18

Solution :

Let n = number of nickels

30 - n = number of quarters

0.05 + 0.25(30 - n) = 4.70

0.05 + 7.5 - 0.25n = 4.70

0.2n = 7.5 - 4.70

0.2n = 2.8

n = 14

So, option (C) is correct.

Problem 5 :

Express, in terms of x, the value, in cents, of x pounds of 40 cent cookies and (30 -x) pounds of 50 cents cookies.

A) 150 + 10x      B) 150 - 50x       C) 1500 - 10x

D) 1500 - 50x          E) 1500 + 10x

Solution :

x pounds of 40 cent cookies.

Worth of it = 0.40x --(1)

30-x of 50 cents cookies.

worth of it = 0.50(30 - x) --(2)

(1) + (2)

Total worth = 0.40x + 0.50(30 - x)

= 0.40x + 15 - 0.50x

= -0.10x + 15

To convert in to cents, we have to multiply by 100.

= 1500 - 10x

So, option (C) is correct.

Problem 6 :

How many pounds of nuts selling for 70 cents a pound must be mixed with 30 pounds of nuts selling at 90 cents a pound to make a mixture that will sell for 85 cents a pound?

A) 7.5           B) 10         C) 22.5            D) 40     E) 12

Solution :

Let x be the quantity of nuts cost 0.70 a pound.

0.70x + 30(0.90) = (x + 30)0.85

0.70x + 27 = 0.85x + 25.5

0.70x - 0.85x = 25.5 - 27

0.15 x = 1.5

x = 1.5/0.15

x = 10

Problem 8 :

A solution of 60 quarts of sugar and water is 20% sugar. How much water must be added to make a solution that is 5% sugar?

A) 180 qts.     B) 120 qts.     C) 100 qts. 

 D) 80 qts.       E) 20 qts.

Solution :

Let x be the required quantity of water to be added.

12 = 5% of (60 + x)

12 = 0.05(60 + x)

12 = 3 + 0.05x

12 - 3 = 0.05x

9 = 0.05x

x = 9/0.05

x = 180

So, option (A) is correct.

Problem 9 :

How much water must be evaporated from 240 pounds of a solution that is 3% alcohol to strengthen it to a solution that is 5% alcohol?

A) 120lbs      B) 96 Ibs       C) 100 Ibs

D) 84 Ibs       E) 140 Ibs

Solution :

Originally had 240 pounds of solution. Let x be quantity of water evaporated.

Remaining quantity of water = 240 - x

7.2 = 5% of (240 - x)

7.2 = 0.05 (240 - x)

7.2 = 12 - 0.05x

0.05x = 12 - 7.2

0.05x = 4.8

x = 4.8/0.05

x = 96

So, option (B) is correct.

Problem 10 :

A container holds 10 pints of a solution which is 20% acid. If 3 quarts of pure acid are added to the container, what percent of the resulting mixture is acid?

A) 5      B) 10     C) 20      D) 50      E) 33 1/3

Solution :

1 quart = 2 pints

3 quart = 6 pints

10 pints + 6 pints = 16 pints

20% of 10 = 2

Original quantity = 16, new quantity = 8

= 8/16

Converting into percentage = (8/16) x 100%

= 50%

So, option (E) is correct.