SOLUTION: Can you help me get the answer and equation for this problem? Penny collected some change in preparation for a garage sale. She collected two more nickels than twice the numbe

Question 168398: Can you help me get the answer and equation for this problem?
Penny collected some change in preparation for a garage sale. She collected two more nickels than twice the number of dimes and eight fewer quarters than twice the number of nickels. If the value of the quarters was $1.60 greater than four times the value of the nickels and dimes together, what was the total value of the change that Penny collected?

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=number of nickels; 2x=twice the number of nickels; 2x-8 would be 8 fewer than twice the number of nickels
y=number of dimes; 2y=twice the number of dimes; 2y+2=2 more than twice the number of dimes
z=number of quarters
Now lets deal in pennies instead of $.
Value of the nickels=5x
Value of the dimes=10y
4 times the value of the nickels and dimes together=4(5x+10y)
Value of the quarters=25z
Now we are told the following:
x=2y+2 -------------------eq1
z=2x-8 ---------------------eq2
and
25z=4(5x+10y)+160-------------------------eq3
Lets rearrange and simplify the above equations so we can see what we are dealing with:
x-2y =2---------------------eq1
2x -z=8---------------------eq2
4x+8y-5z=-32-------------------eq3
Multiply eq1 by 4 and add it to
eq3 and we get:
8x-5z=-24----------------------------eq3a
Next multiply eq2 by 4 and subtract it from eq3a and we get
(8x-5z+-24) -(8x-4z=32) or
-z=-56
z=56-------------------------------------------number of quarters
substitute z=56 into eq2 and we get:
2x-56=8
2x=64
x=32-------------------------------------number of nickels
substitute x=32 into eq1 and we get:
32-2y=2
-2y=-30
y=15------------------------------------- number of dimes
CK
two more nickels than twice the number of dimes:
2*15+2=32
32=32
eight fewer quarters than twice the number of nickels:
32*2-8=56
56=56
value of the quarters was $1.60 greater than four times the value of the nickels and dimes together:
56*25=4(32*5+15*10)+160
1400=4(160+150)+160=(4*310)+160
1400=1240+160=1400
1400=1400
Hope this helps-----ptaylor

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