SOLUTION: I have 100 coins that will equal $5. The denomination of coins is half dollars, dimes and pennies. What is the brake down?

Question 360042: I have 100 coins that will equal $5. The denomination of coins is half dollars,
dimes and pennies. What is the brake down?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
I have 100 coins that will equal $5.
The denomination of coins is half dollars, dimes and pennies.
:
Let p = no. of pennies
Let d = no. of dimes
let h = no. of halfs
:
Two equations (but 3 unknowns)
p + d + h = 100
:
.01p + .10d + .50h = 5.00
Get rid of the decimals, multiply by 100
p + 10d + 50h = 500
:
Subtract the 1st equation from the above equation
p + 10d + 50h = 500
p + d + h = 100
--------------------Subtraction eliminates p
9d + 49h = 400
9d = -49h + 400
d = h +
We know that the values of d and h have to be integers, and
that the no. of halfs (h) has to be a low single digit number
Let h = 1
d = (1) +
d = +
d = (351 is a multiple of 9)
d = 39 dimes
We have 39 dimes and 1 half
Find p
p = 100 - 40
p = 60 pennies
:
60 pennies, 39 dimes and 1 half
:
:
Check in the value equation:
.01(60) + .10(39) + .50(1) =
.60 + 3.90 + .50 = 5.00
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