Question 75604
Addie has $2.15 in her change purse, consisting of nickels, dimes, and quarters.
:
The equation:
.05n + .10d + .25q = 2.15
;
Write an equation for each phrase:
"If she has twice as many nickels as quarters"
n = 2q
:
" and one less dime than quarters,"
d = (q - 1)
:
We can put everything in terms of q and solve for that:
Substitute 2q for n, (q-1) for d) in the original equation:
:
.05(2q) + .10(q-1) + .25q = 2.15
.1q + .1q - .1 + .25q = 2.15
.45q = 2.15 + .1
.45q = 2.25
q = 2.25/.45
q = 5 quarters
:
n = 2(5) = 10 nickels
:
d = 5 - 1 = 4 dimes
:
:
Check: .05(10) + .1(4) + .25(5) =
.5 + .4 + 1.25 = 2.15, check our solutions
:
Make sense to you?