Question

Andy has $20 and earns $5 per week selling candy. Jennifer has $50 and earns $2 per week selling chocolate.

How many weeks until Andy and Jennifer have the same amount of money?

Answer 1

10 weeks

Explanation:

Linear Equations

There are situations where one variables is related in one equation and we need to find its value by solving the equation. There are many techniques available to solve it.

The conditions of the problem state that Andy has $20 and earns $5 per week selling candy. If
`M_1` is the amount of money Andy has when x weeks have passed, then

`\displaystyle M_1=20+5x`

We also know that Jennifer has $50 and earns $2 per week selling chocolate. If
`M_2` is the amount of money she has after x weeks, then

`\displaystyle M_2=50+2x`

They will have the same amount of money when

`\displaystyle M_1=M_2`

Or equivalently

`\displaystyle 20+5x=50+2x`

Rearranging

`\displaystyle 5x-2x=50-20`

Simplifying

`\displaystyle 3x=30`

Solving for x

`\displaystyle x=10`

As for checking, Andy will have

`\displaystyle M_1=20+5(10)=$70`

`\displaystyle M_2=50+2(10)=$70`