Posted by Jasmine on .
There are 52 coins that consists of pennies, dimes, and quarters. Two stacks have the same number of coins and the third stack has twice as much. The coins equal to $5.98. How many pennies, dimes, and quarters are there? I already found out that two stacks have 13 coins and one stack has 26 coins.
Since you already have the second part, let's work on the number of pennies , dimes and quarters we have to make $5.98
number of pennies -- x
number of dimes ---- y
number of quarters -- 52-x-y
x + 10y + 25(52-x-y) = 598
x+10y + 1300 - 25x - 25y = 598
-24x - 15y = -702
8x + 5y = 234
y = (234 - 8x)/5
by trial and error, I found the smallest integer value to work is
x = 3, y = 34
since the slope of 8x+5y=234 is -8/5 ,
increasing the x by 8 and decreasing the y by 5 has to give me another solution,
So I got the following:
P D Q
3 34 10
13 26 13
18 18 16
23 10 19
28 2 20
So there are 5 different solutions to your problem
testing each, you can see that you get a sum of $5.98 for each one.
e.g. 23 pennies, 10 dimes and 19 quarters
= 23 + 10(10) + 25(19) = 598
Your question does not specify what type of coins each stack must contain.
An interesting addition to the problem would be to insist that each stack consists of the same denomination of coins in the ratio of 1 : 1 : 2
Would this be even possible??
so the answer is 28 pennies 7 dimes and 5 sets of quarters