Question 155215: You have a total of $4564.50 in coins. There are 8 times as many half-dollars as quarters and 6 times as many dimes as nickels. How many coins were there of each kind
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! You have a total of $4564.50 in coins. There are 8 times as many half-dollars as quarters and 6 times as many dimes as nickels. How many coins were there of each kind?
:
We have 4 unknowns and only 3 equations here. There is more than one solution.
:
Simplify as much as we can:
.05n + .10d + .25q + .50h = 4564.50
:
It says: h = 8q, and d = 6n, substitute for h and d in the above equation:
:
.05n + .10(6n) + .25q + .50(8q) = 4564.50
:
.05n + .60n + .25q + 4q = 4564.50
:
.65n + 4.25q = 4564.50
:
Using a calc, I found a value for q that gives an integer value for n:
Let q = 450 quarters.
then
.65n + 4.25(450) = 4564.50
.65n + 1912.50 = 4564.50
.65n = 4564.50 - 1912.50
.65n = 2652
n = 
n = 4080 nickels
:
Find the no. of dimes:
d = 6*4080
d = 24480 dimes
:
Find no. of half dollars
h = 8*450
h = 3600 half dollars
:
:
Check solutions total:
.05(4080) + .10(24480) + .25(450) + .5(3600) =
204 + 2448 + 112.50 + 1800 = 4564.50
:
However, there are many other solutions, you can check using other values for q:
q = 34, 47, 60, 73, 86, 99, 112, 125; you can see starting at 34, every 13th no.
will give an integer value for n.
|
|
|
