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Mr. Collins and Ms. LaPointe are saving money to buy a new motorcycle. The total amount of money Mr. Collins will save is given by the function p(x) = 62 + 5x. The total amount of money Ms. LaPointe will save is given by the function a(x) = x2 + 38. After how many months, x, will they have the same amount of money saved?

User Alex Li
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We have been given that Mr. Collins and Ms. LaPointe are saving money to buy a new motorcycle. The total amount of money Mr. Collins will save is given by the function
p(x) = 62+5x. The total amount of money Ms. LaPointe will save is given by the function
a(x) = x^2+38. We are asked to find number of months when they have the same amount of money saved.

To solve our given problem, we will equate both equations as:


x^2+38=62+5x


x^2-5x+38=62+5x-5x


x^2-5x+38=62


x^2-5x+38-62=62-62


x^2-5x-24=0


x^2-8x+3x-24=0


x(x-8)+3(x-8)=0


(x-8)(x+3)=0


(x-8)=0,(x+3)=0


x=8,x=-3

Since time cannot be negative, therefore, after 8 months they will have the same amount of money saved.

User Amgaera
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