Question

Sarah has a collection of nickels, dimes, and quarters worth $28.75. She has 10 more dimes than nickels and twice as many quarters as dimes. How many coins of each kind does she have?

nickels:
dimes:
quarters:

Answer 1

Explanation:

Write an equation for each statement:

:

"Sarah has a collection of nickels, dimes, and quarters worth $15.75."

.05n + .1d + .25q = 15.75

:

"She has 10 more dimes than nickels"

d = n + 10

:

"twice as many quarters as dimes."

q = 2d

:

How many coins of each kind does she have?

:

Take the 2nd equation and arrange it so n is in terms of d also

n + 10 = d

n = (d - 10)

:

In the 1st equation substitute (d-10) for n and 2d for q:

.05n + .1d + .25q = 15.75

:

.05(d-10) + .1d + .25(2d) = 15.75

:

.05d - .5 + .1d + .5d = 15.75

:

.65d - .5 = 15.75

:

.65d = 15.75 + .5

:

.65d = 16.25

:

d = 16.25/.65

:

d = 25 dimes

:

Remember the statement "twice as many quarters as dimes."

q = 2(25)

q = 50 quarters

:

The statement "She has 10 more dimes than nickels"

n = 25 - 10

n - 15 nickels

:

Check our solutions

.05(15) + .1(25) + .25(50) =

.75 + 2.50 + 12.50 = 15.75 proves our solutions