SOLUTION: The value of a pile of pennies, dimes, and quarters is $21.92. The ratio of the number of pennies to dimes is 4 to 7. The ratio of the number of dimes to quarters is 7 to 8. How

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: The value of a pile of pennies, dimes, and quarters is $21.92. The ratio of the number of pennies to dimes is 4 to 7. The ratio of the number of dimes to quarters is 7 to 8. How      Log On


   

Question 162954: The value of a pile of pennies, dimes, and quarters is $21.92. The ratio of the number of pennies to dimes is 4 to 7. The ratio of the number of dimes to quarters is 7 to 8. How many pennies, dimes, and quarters are in the pile?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Write equations for each statement:
p = no. of pennies
d = no. of dimes
q = no of quarters
:
"The value of a pile of pennies, dimes, and quarters is $21.92."
.01p + .10d + .25q = 21.92
:
" The ratio of the number of pennies to dimes is 4 to 7."
p%2Fd = 4%2F7
Cross multiply
7p = 4d
p = 4%2F7d
:
" The ratio of the number of dimes to quarters is 7 to 8."
d%2Fq = 7%2F8
Cross multiply
7q = 8d
q = 8%2F7d
:
How many pennies, dimes, and quarters are in the pile?
:
Substitute for p & q in the total$ equation
.01*4%2F7d + .10d + .25*8%2F7q = 21.92
Multiply equation 7, results:
.01(4d) + 7(.10d) + .25(8q) = 7(21.92)
:
.04d + .70d + 2.00q = 153.44
:
2.74d = 153.44
d = 153.44%2F2.74
d = 56 dimes
:
p = 4%2F7*56
p = 32 pennies
and
q = 8%2F7*56
q = 64 quarters
;
:
Check solution:
.01(32) + .10(56) + .25(64) =
.32 + 5.60 + 16.00 = 21.92; confirms our solution