Variables on both sides

Question

Suppose you receive an allowance of $79 and your friend receives an allowance of $59 at the beginning of the month. If you spend $9 a day and your friend spends $4 a day, after how many days will you and your friend have the same amount of money?

Answer 1

Hi Angelica,

So first you want to set up what your variable will be. Since number of days is the variable we are after, lets call that "d".

Next: You had 79 dollars and your friend had 59 dollars in the beginning of the month. You spent 9 dollars a day (9 x d, or 9d). Your friend spend 4 dollars a day (4d).

You want to know how many days will make the two sides equal. So

you: 79 - 9d (start with 79 and subtract 9 dollars each day)

your friend 59 - 4d (start with 59 and subtract 4 dollars each day)

These are set to equal each other.

79 - 9d = 59 - 4d

Then compute.

-59 on both sides

20 - 9d = - 4d

+ 9d to both sides

20 = 5d

divide by 5 on both sides

4 = d

4 days!