Question

Lisa and Joey are each saving money for their prom. Lisa’s total amount of money is represented by the function f(x)=20-13x. The total amount of money Joey has is given by the function g(x)=x^2-10. After how many weeks, x, will they have the same amount of money saved? Show your work.

Answer 1

2 weeks

Explanation:

Given in the question that,

Equation that represent Lisa's total amount of money

f(x) = 20 - 13x

Equation that represent Joey's total amount of money

g(x) = x² - 10

To find weeks, x, after which they will have same amount of money, we will equate both equation

20 - 13x = x² - 10

x² - 10 - 20 + 13x = 0

x² - 30 + 13x = 0

x² + 13x - 30 = 0

(x - 2)(x + 15) = 0

x = 2 or x = -15

Weeks, x, can not be negative so we will reject x = -15

Hence, after 2nd week Lisa and Joey will have the same amount of money save.