Question

Gabe and Caden mow lawns in their neighborhood on the weekends to earn extra money. They are both saving money for a new game system. Gabe's savings can be represented by the equation 8 = 40t + 50, where t is the time, in weeks, since he started saving. Caden's savings are given by the equation 8 = 35t + 100. Which of the following statements correctly interprets the meaning of the solution to the system of equations in this context?

Option 1: Gabe and Caden both have $450 saved after 10 weeks of saving their money from mowing lawns.
Option 2: Gabe and Caden both have $170 saved after 2 weeks of saving their money from mowing lawns.
Option 3: Gabe and Caden both have $130 saved after 2 weeks of saving their money from mowing lawns.
Option 4: Gabe and Caden both have $510 saved after 450 weeks of saving their money from mowing lawns.

Answer 1

The solution to the system of equations is that Gabe and Caden both have $130 saved after 2 weeks of saving their money from mowing lawns.

Step-by-step explanation:

The given equations are:

Gabe: 8 = 40t + 50

Caden: 8 = 35t + 100

To find the meaning of the solution to the system of equations, we need to find the values of t for which the equations are true.

By solving the first equation, we get: 40t = -42, t = -1.05

By solving the second equation, we get: 35t = -92, t = -2.63

Option 3: Gabe and Caden both have $130 saved after 2 weeks of saving their money from mowing lawns.