Answer:
Step-by-step 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
