Question 622613
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
{{{x=y-14}}}
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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
{{{60-x=y-40}}}
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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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{{{60-x=y-40}}}
{{{60-(y-14)=y-40}}}
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Simplify and solve for y.
{{{60-y+14=y-40}}}
{{{-y+74=y-40}}}
{{{-2y+74=-40}}}
{{{-2y=-114}}}
{{{y=57}}}
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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