Let 'x' be Carol's age at present
'y' be her brother's age at present
Two years from now:
Let 'x+2' be Carol's age two years from now
'y+2' be her brother's age two years from now
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Carol is five times as old as her brother
x = 5y ------equation 1
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she will be three times as old as her brother in two years
x + 2 = 3(y+2) ----equation 2
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From equation 2:
x+2= 3(y+2)
x+2 = 3y + 6
x = 3y + 6 - 2
x = 3y + 4 -----equation 3
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Substitute equation 3 to equation 1
x = 5y
3y + 4 = 5y
5y - 3y = 4
2y = 4
y = 2
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Substitute y=2 to equation 1
x = 5y
x = 5(2)
x = 10
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Therefore at present,Carol is 10 years old while her brother is 2 years old.
