Question

alice has eight good behavior stars and earns a new one each week. Mack has two good behavior stars and earns two new ones each week. In how many weeks will they have the same number of good behavior stars?

Answer 1

In 14 weeks will they have the same number of good behavior stars

Explanation:

Let

x ----> the number of weeks

y ----> the number of good behavior stars

we know that

Alice

`y=x+8` ----> equation A

Mack

`y=2x+2` ----> equation B

To find out in how many weeks will they have the same number of good behavior stars, equate equation A and equation B

`2x+2=x+8`

Solve for x

`2x-x=8-2`

`x=6\ weeks`

Verify

For x=6 weeks

Alice

`y=(6)+8=14\ stars`

Mack

`y=2(6)+2=14\ stars`

therefore

In 14 weeks will they have the same number of good behavior stars