SOLUTION: Joe is 10 years older than James. In 8 years, twice Joe's age will equal three times James's age. How old is each now?

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Question 614351: Joe is 10 years older than James. In 8 years, twice Joe's age will equal three times James's age. How old is each now?
Answer by Maths68(1474) (Show Source):
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Let
Present age of Joe = x
Present age of James = y

Joe is 10 years older than James
x=y+10..............(1)

In 8 years
Joe will be = x+8
James will be = y+8

Then
twice Joe's age will equal three times James's age
2(x+8)=3(y+8)
2x+16=3y+24
2x-3y=24-16
2x-3y=8.................(2)

Substituent the value of x from (1) to (2)
2x-3y=8
2(y+10)-3y=8
2y+20-3y=8
2y-3y=8-20
-y=-12
Cancel out (-)
y=12

Put the value of y in (1)
x=y+10
x=12+10
x=22

Present age of Joe = x = 22 years old
Present age of James = y = 12 years old