Question 1190483
Woman's age = W
Daughter's age = D
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<u>Make two equations:</u>
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W = D + 25
W - 3 = 3(D - 3)
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<u>Simplify the second equation:</u>
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W = D + 25
W - 3 = 3D - 9
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<u>Move the variables to left side and the constants to right side:</u>
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W - D = 25
W - 3D = -6
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<u>Multiply the first equation by -3:</u>
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-3W + 3D = -75
W - 3D = -6
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<u>Add the equations together:</u>
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-2W = -81
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<u>Solve for W:</u>
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W = 40.5
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<u>Substitute W = 40.5 into either of the original equations:</u>
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W = D + 25
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40.5 = D + 25
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<u>Solve for D:</u>
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D = 15.5
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Woman's age = W = <b>40.5</b>
Daughter's age = D = <b>15.5</b>
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<u>Check it:</u>
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<i>"A woman is older than her daughter by 25 years."</i>
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40.5 is 25 years older than 15.5.
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<i>"Three years ago, the ratio of their ages was 3:1."</i>
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Three years ago, the woman was 37.5 and the daughter was 12.5.  The ratio of 37.5 to 12.5 is 3:1.