Question

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?

Answer 1

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.