Asked by john
If 25 times were moved from Box A to Box B, there would be an equal number of dimes in both boxes. If 100 dimes were moved from Box B to Box A, the ratio of dimes in Box A to Box B would be 7:2. What was the original number of dimes in Box A?
Answers
Answered by
Reiny
dimes in box A originally --- x
dimes in box B originally --- y
case 1:
after 25 moved from A to B
box A has x-25
box B has y+25
but x-25 = y+ 25 ----> x = y + 50
case 2:
after 100 dimes moved from B to A
box A has x+100
box B has y-100
but (x+100)/(y-100) = 7/2
7y - 700 = 2x + 200
7y - 2x = 900
7y - 2(y+50) = 900
5y = 1000
y = 200
then x = 250
there were 250 dimes in box A
dimes in box B originally --- y
case 1:
after 25 moved from A to B
box A has x-25
box B has y+25
but x-25 = y+ 25 ----> x = y + 50
case 2:
after 100 dimes moved from B to A
box A has x+100
box B has y-100
but (x+100)/(y-100) = 7/2
7y - 700 = 2x + 200
7y - 2x = 900
7y - 2(y+50) = 900
5y = 1000
y = 200
then x = 250
there were 250 dimes in box A
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