Question 319127: Tim has $5.03 in quarters, nickels, dimes, pennies, and half-dollars in a desk drawer. He has fice more nickles than quarters, then number of pennies is two-thirds the number of nickles, there are half as many half-dollars as pennies, and half as many dimes as nickels. How many coins of each type does he have?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Tim has $5.03 in quarters, nickels, dimes, pennies, and half-dollars in a desk drawer.
He has five more nickles than quarters, then number of pennies is two-thirds
the number of nickles, there are half as many half-dollars as pennies,
and half as many dimes as nickels.
How many coins of each type does he have?
:
Write a equation for each statement:
"Tim has $5.03 in quarters, nickels, dimes, pennies, and half-dollars in a desk drawer."
.01p + .05n + .10d + .25q + .50h = 5.03
:
"He has five more nickles than quarters,"
n = q + 5
or
q = n - 5
:
"then number of pennies is two-thirds the number of nickles,"
p =  n
:
"there are half as many half-dollars as pennies,"
h =  p
replace p with n
h = *n
h =  n
:
" half as many dimes as nickels."
d = .5n
:
.01p + .05n + .10d + .25q + .50h = 5.03
get rid of the decimals, multiply by 100
p + 5n + 10d + 25q + 50 = 503
Get everything in terms of n, replace p, d, q, and h
n + 5n + 10(.5n) + 25(n-5) + 50*n = 503
multiply by 3, get rid of the fractions
2n + 15n + 30(.5n) + 75(n-5) + 50n = 1509
:
2n + 15n + 15n + 75n - 375 + 50n = 1509
:
157n = 1509 + 375
:
157n = 1884
n = 
n = 12 nickels
:
How many coins of each type does he have?
p:*12 = 8 pennies
:
h: *12 = 4 half dollars
:
q: 12 - 5 = 7 quarters
:
d: .5(12) = 6 dimes
:
:
Check the solutions, find the total
.01(8) + .05(12) + .10(6) .25(7) + .50(4) =
.08 + .60 + .60 + 1.75 + 2.00 = 5.03; confirms our solutions
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