Question 462031
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Let *[tex \Large x] represent Jenny's age today.  Let *[tex \Large y] represent John's age today.  Then *[tex \Large x\ -\ 5] is Jenny's age 5 years ago, and *[tex \Large y\ -\ 5] is John's age 5 years ago.  Likewise, *[tex \Large x\ +\ 5] is Jenny's age 5 years from now, and *[tex \Large y\ +\ 5] is John's age 5 years from now.


We have to make assumptions about the conditions stated in the problem because there are ambiguities in the language.  I'm going to re-write it expressing the assumptions and eliminating the ambiguities.


<i>Five years ago Jenny was exactly double the age of John <u>at that time</u>. Five years from now John will be exactly 3/4 the age <u>that</u> Jenny <u>will be at that time</u>.  Calcute both their ages.</i>


Using the stated conditions, establish two equality relationships:



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ -\ 5\ =\ 2(y\ -\ 5)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{3}{4}(x\ +\ 5)\ =\ y\ +\ 5]


Solve the system for *[tex \Large x], Jenny's age now, and *[tex \Large y], John's age now.  Hint:  Rearrange both equations into standard form, then solve by elimination using a multiplier of -2 on the first equation.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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