Currently, you have $60 and your sister has $135. You decide to save $5 of your allowance each week, while your sister decides to spend her whole allowance plus $10 each week. How long will it be before you have as much money as your sister?

It will take 5 weeks for both to have the same amount of savings.

It takes a lot longer to explain what is going on than to do the actual maths with shortcuts.

Explanation:

Let the count of weeks be

w

You start off with $60 in your savings

This is increased by $5 each week so the total in your savings at any given count of weeks count is:

$

60

+

$

5

w

... Equation (1)

...

Your sister does not add to her savings but reduces it by $10 each week. So her savings at any given week count is:

$

135

-

$

10

w

... Equation (2)

...

The count of weeks when both savings are equal is defined by the model:

Equation (1) = Equation (2)

60

+

5

w

=

135

-

10

w

←

in dollars

Add

10

w

to both sides

60

+

5

w

+

10

w

=

135

Subtract 60 from both sides

5

w

+

10

w

=

135

-

60

Simplify

15

w

=

75

Divide both sides by 15

Did you know you can treat units of measurement ($) the same way you do the numbers.

w

=

$

75

$

15

→

.

75

15

$

$

The $ signs cancel out so you are only left with numbers

w

=

75

15

→

75

:

15

15

:

15

=

5

1

=

5

w

=

5