Question 622613: Mrs. West is 14 years younger than her aunt. If Mrs. West's age in years is as much below 60 as her aunt's age is over 40. How old is each person?
I know the answer is aunt = 57
And West's = 43
But I don't know HOW they got the answer. Can you show me the steps please?
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! Hi, there--
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Here are the steps:
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Let x be Mrs. West's age.
Let y be her aunt's age.
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Now we need to write two equations using the information in the problem to model the situation.
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In algebra, the phrase, "Mrs. West is 14 years younger than her aunt," can be written as
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The phrase, "Mrs. West's age in years is as much below 60 as her aunt's age is over 40," can be written as
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(Fortunately, no one talks like this in real life!)
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Now we have a system of equations. We'll use the substitution method to solve it. Substitute y-14 for x in the second equation. (This substitution comes from the first equation.)
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Simplify and solve for y.
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In the context of our problem, the equation y=57 means that the aunt is 57 years old. Since Mrs. West is 14 years younger, she is 57-14=43 years old.
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As a last step, we need to check our answers against that bizarre sentence in the the original problem: Mrs. West's age in years is as much below 60 as her aunt's age is over 40. "57 years" is as much below 60 as "43 years" is over 40. Yes, 60-57=3 and 43-40=3. Check!
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Feel free to email if you still have questions about this.
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Ms.Figgy
math.in.the.vortex@gmail.com
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