Question

Tyrone has $60 and his sister has $135. Both get an allowance of $5 per week. He decides to save his entire allowance. His sister spends all of hers each week plus an additional $10. After how many weeks will each have the same amount of money?

Answer 1

After 5 weeks

Explanation:

Let x be the number of weeks:
`x="number of weeks"`

Now putting the problem in an equation in terms of x:

`"Tyrone":60+5x`
Since tyrone has 60$ and it is increasing by 5 every week

`"Sister":135cancel(+5x)cancel(-5x)-10x`
Since his sister is spending her allowance and an extra 10$

To be equal:
`60+5x=135-10x`

Adding 10x to both sides:
`60+5x+10x=135cancel(-10x)cancel(+10x)`
`60+15x=135`

Subtracting 60 from both sides:
`cancel60cancel(-60)+15x=135-60`
`15x=75`

Dividing both sides by 15
`(cancel15x)/cancel15=75/15`
`rArrx=5`