SOLUTION: Hi Jack had some 20cent and 10cent coins. When he used 1/3 of them he had $9.60 left. He used half as many 20cent as 10 cent coins. How many 20 cent coins did he use. Than

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Question 1168246: Hi
Jack had some 20cent and 10cent coins. When he used 1/3 of them he had $9.60 left. He used half as many 20cent as 10 cent coins.
How many 20 cent coins did he use.
Thanks
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let the number of 20cent coins be x and the number of 10cent coins y
amount of money is 0.20x and 0.10y
he has x%2By coins all together which gives him $0.20x%2B0.10y
when he used 1%2F3 of them he had $9.60 left
0.20x%2B0.10y+-%281%2F3%29%280.20x%2B0.10y%29=9.60.....both sides multiply by 3
0.60x%2B0.30y+-%280.20x%2B0.10y%29=3%2A9.60
0.60x%2B0.30y+-0.20x-0.10y=28.80
0.4x+%2B+0.2y=28.80......both sides multiply by 10
4x+%2B+2y=288.....both sides divide by 2
2x+%2B+y=144
if he used half as many 20cent as 10 cent coins, then x=y%2F2
substitute and solve for y
2%28y%2F2%29+%2B++y=144
y+%2B++y=144
2y=144
highlight%28y=72%29-> the number of 10cent coins
and
x=y%2F2
x=72%2F2
highlight%28x=36%29->the number of 20cent coins

check:
0.20x%2B0.10y=0.20%2A36%2B0.10%2A72=14.40
if he he used 1%2F3 of them he had $9.60 left
14.40+-%281%2F3%29%280.20%2A36%2B0.10%2A72%29=9.60
14.40+-4.80=9.60
9.60=9.60->true