SOLUTION: Samantha has a total of one hundred forty-one pennies,nickels and quarters.She has a total of $15.17. She has fifteen more quarters than pennies and fifteen fewer quarters than nic

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Question 140141: Samantha has a total of one hundred forty-one pennies,nickels and quarters.She has a total of $15.17. She has fifteen more quarters than pennies and fifteen fewer quarters than nickels. How many of each coin does she have?
Found 2 solutions by scott8148, ankor@dixie-net.com:
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
"a total of one hundred forty-one pennies,nickels and quarters" __ 141=p+n+q

"She has a total of $15.17" __ 1p+5n+25q=1517

"fifteen more quarters than pennies" __ q-15=p

"fifteen fewer quarters than nickels" __ q+15=n

substituting __ 141=(q-15)+n+q __ 156=2q+n

substituting __ 156=2q+(q+15) __ 141=3q __ 47=q

substituting __ 47+15=n __ 62=n

substituting __ 47-15=p __ 32=p

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Write an equation for each statement:
;
Samantha has a total of one hundred forty-one pennies,nickels and quarters.
p + n + q = 141
:
She has a total of $15.17.
.01p + .05n + .25q = 15.17
:
She has fifteen more quarters than pennies
p = q - 15
:
and fifteen fewer quarters than nickels.
n = q + 15
:
how many of each coin does she have?
:
Replace p with (q-15) and n with (q+15); find q
.01(q-15) + .05(q+15) + .25q = 15.17
:
.01q - .15 + .05q + .75 + .25q = 15.17
:
.31q + .60 = 15.17
:
.31q = 15.17 - .60
:
.31q = 14.57
q =
q = 47 quarters.
:
p = 47 - 15 = 32 pennies
and
n = 47 + 15 = 62 nickels
:
:
Check solution by finding the number of coins:
32 + 62 + 47 = 141 coins