Question

5. Brooke does Valeria's nails every week. Valeria has

$30 and is spending $7 per session. Brooke has $10 and
is gaining $7 per session. After how many weeks will the
two girls have the same amount?

Answer 1

1.429 Weeks

Explanation:

This problem is asking for the intersection point of two lines, or a systems of equations.

We know Valeria has 30 dollars to begin with, and spends 7 per session, meaning she loses 7 per session. Therefore her equation would be:

`y=30-7x`

Brooke has 10 dollars, and gains 7 for every session Valeria attends. So her equation would be:

`y=10+7x`

Knowing they both equal y we also know they are equal to each other, so lets create an equation and solve.

We start with the equation

`30-7x=10+7x`

Lets subtract 10 from both sides

`20-7x=7x`

Now add 7x to both sides

`20=14x`

Now divide both sides by 14 to get the value of x

`(20)/(14) =x`

This can be simplified to

`(10)/(7)`

Or approximately

1.429