Can someone help me answer this question

Question

. Sarah begins the year with $100 in her savings account. Each week, she spends $8. Martin begins the year with no money saved, but each week he puts $12 in an account. Let x represent the number of weeks that have passed since the beginning of the year. How many weeks will have passed when they have the same amount of money in their accounts? Show all work necessary to justify your answer.

Answer 1

Let the equation to represent Sarah's savings be 100 - 8x.

The equation for Martin's account would be 12x.

We are looking for the week, x, in which the two accounts have the same amount of money.

To find this, we simply need to set the equations equal to each other: 100-8x = 12x.

Now we only need to solve for x.

Add 8x to both sides: 100 = 20x

Divide both sides by 20: x = 5

After 5 weeks, Martin and Sarah will have the same amount of money in their accounts. If you need to find how much that would be, you can plug your x value into either equation.