Chayil H.

asked • 06/01/16

can you help me with my hw

John and Sarah are each saving money for a car. The total amount of money John will save is represented by the function       f(x) = 60 +5x. The total amount of money Sarah will save is given by the function g(x)=x^2 +46. after how many weeks, x, will they have the same amount of money saved? explain how you arrived at your answer.

1 Expert Answer

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Richard C. answered • 06/01/16

Yes, You Can Learn Math!

Chayil H.

why do you need to factor?
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06/01/16

Richard C.

Chayil,
 
Any quadratic function (the largest power of x is 2 like the one in your problem) has two solutions.  A quadratic, when graphed, looks like a parabola.  Sometimes, the parabola crosses the x-axis at two places: two solutions for x.
 
In the case here, we needed to factor the quadratic to find what the two x's are.  Any quadratic factored will look like:
 
(ax + c)(bx + c)
 
The two factors we found have this appearance.  The reason we only used one of them is because we needed to find weeks and that can't be negative.
 
Make sense?
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06/01/16

Richard C.

meant (ax + c)(bx + d).
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06/01/16

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