# 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?

1
by jamesmanzano

2014-11-13T22:19:50+08:00
Let 'x' be Perla's age at present
'y' be Merly's age at present
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Two years ago their ages were:
x - 2   ----Perla
y - 2   ----Merly
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Two years from now their ages will be:
x + 2  ----Perla
y + 2  ----Merly
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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
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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
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equate equations 1 and 2
7y - 12 = 4y + 12
7y - 4y = 12 + 12
3y = 24
y = 8
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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.