Question

There are two less nickels than dimes, and as many quarters, as nickels and dimes together. The total amount of money is $5.25. How many quarters, dimes, and nickels are there?

Answer 1

There are 7 nickels, 9 dimes, and 16 quarters. If you do the math 7 nickels equals 35 cents, 9 dimes equal 90 cents, and 16 quarters equals $4.00, which all adds up to $5.25. Also the numbers follow the rules because 7 is two less than nine and 16 is 9+7. 

Answer 2

The number of nickel = 7

The number of dimes = 7 + 2 = 9

The number of quarters = 2 × 7 + 2 = 16

Explanation:

1 dime = $0.10

1 nickel = $0.05

1 quarter = $0.25

number of dime = a + 2

number of nickel = a

number of quarter = a + a + 2 = 2a + 2

Total amount = $5.25

The total amount can be represented base on the information from the question as

(a + 2)0.10 + (a)0.05 + (2a + 2)0.25 = 5.25

0.10a + 0.20 + 0.05a + 0.5a + 0.5 = 5.25

0.65 a + 0.70 = 5.25

0.65a = 5.25 - 0.70

0.65a = 4.55

a = 4.55/0.65

a = 7

The number of nickel = 7

The number of dimes = 7 + 2 = 9

The number of quarters = 2 × 7 + 2 = 16