Question
The ratio of the number of one dollar coins in a box was 3:4.six one dollar coins were removed & some fifty cent coins of the same amount were added.the ratio of the number of one dollar coins to the number of fifty cent coins then became 1:3.what was the total amount of money in the box?
Answers
Steve
if there were x 50-cent coins and y dollar coins, then if 6 dollars were replaced with 12 halves,
x/y = 3/4
(x-6)/(y+12) = 1/3
clearing the fractions, we have
4x = 3y
3(x-6) = y+12
4x-3y = 0
3x-y = 30
now we see that y=3x-30, so
4x-3(3x-30) = 0
4x-9x+90 = 0
5x = 90
x = 18
So, there were 18 dollars and 24 halves.
After the replacements, there were 12 dollars and 36 halves.
I expect you can figure out how much money that was.
x/y = 3/4
(x-6)/(y+12) = 1/3
clearing the fractions, we have
4x = 3y
3(x-6) = y+12
4x-3y = 0
3x-y = 30
now we see that y=3x-30, so
4x-3(3x-30) = 0
4x-9x+90 = 0
5x = 90
x = 18
So, there were 18 dollars and 24 halves.
After the replacements, there were 12 dollars and 36 halves.
I expect you can figure out how much money that was.
Julio
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