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