Question

A collection of 30 coins worth $5.50 consists of nickels, dimes, and quarters. There are twice as many dimes as nickels. How many quarters are there?

Answer 1

1.A collection of 30 coins worth $5.50 consists of nickels, dimes, and quarters. There are twice as many dimes as nickels. How many quarters are there?
:
The number of each coin equation:
n + d + q = 30
:
The $ amt equation:
.05n + .10d + .25q = 5.50
:
"There are twice as many dimes as nickels" equation:
d = 2n
:
Substitute 2n for d in both equations
n + 2n + q = 30
and
.05n + .10(2n) + .25q = 5.50
Which is:
3n + q = 30
and
.25n + .25q = 5.50
:
Multiply the above equation by 4 and subtract it from 3n + q = 30
3n + 1q = 30
1n + 1q = 22
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2n + 0q = 8
n = 8/2
n = 4 nickels
:
Then we know that d = 2(4) = 8 dimes
:
Use the coins equation to find q:
4 + 8 + q = 30
q = 30 - 12
q = 18 quarters
:
Check solutions using the $ equation:
.05(4) + .10(8) + .25(18) =
.20 + .80 + 4.50 = 5.50