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Two years ago, Perla was 7 times as old as Merly. Two years from now, Perla will be 6 years more than 4 times as old as Merly will be. Find the present age of each?
Let 'x' be Perla's age at present 'y' be Merly's age at present ------------------------------------------------------- Two years ago their ages were: x - 2 ----Perla y - 2 ----Merly ------------------------------------------------------- Two years from now their ages will be: x + 2 ----Perla y + 2 ----Merly ------------------------------------------------------- From the statement, 'two years ago Perla was 7 times as old as Merly' x - 2 = 7(y - 2) x - 2 = 7y - 14 transpose -2 to the right x = 7y - 14 + 2 x = 7y - 12 -----equation 1 ------------------------------------------------------ From the statement, 'two years from now Perla will be 6 years more than 4 times as old as Merly' x + 2 = 4(y+2) + 6 x + 2 = 4y + 8 + 6 transpose 2 to the right x = 4y + 8 + 6 - 2 x = 4y + 12 -----equation 2 ------------------------------------------------------ equate equations 1 and 2 7y - 12 = 4y + 12 7y - 4y = 12 + 12 3y = 24 y = 8 ------------------------------------------------------ Substitute y=8 to equation 1 x = 7y - 12 x = 7(8) - 12 x = 56 - 12 x = 44 Therefore Perla is 44 yrs old while Merly is 8 yrs old.
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