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 [tex]p(x) = 62+5x[/tex]. The total amount of money Ms. LaPointe will save is given by the function [tex]a(x) = x^2+38[/tex]. 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:
[tex]x^2+38=62+5x[/tex]
[tex]x^2-5x+38=62+5x-5x[/tex]
[tex]x^2-5x+38=62[/tex]
[tex]x^2-5x+38-62=62-62[/tex]
[tex]x^2-5x-24=0[/tex]
[tex]x^2-8x+3x-24=0[/tex]
[tex]x(x-8)+3(x-8)=0[/tex]
[tex](x-8)(x+3)=0[/tex]
[tex](x-8)=0,(x+3)=0[/tex]
[tex]x=8,x=-3[/tex]
Since time cannot be negative, therefore, after 8 months they will have the same amount of money saved.
