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