Question

Duane and mick are saving their money to build a tree house. Duane adds $5 to their piggy bank every other week. Mick adds $2 every week. So far they have saved $45. How many weeks have they been saving their money?

Answer 1

Duane adds $5 to the piggy bank every other week.
Mick adds $2 to the piggy bank every week.

Duane adds $2.50 to the piggy bank every week.
Mick adds $2 to the piggy bank every week.

Every week, Duane and Mick put in a total of $4.50.

In x weeks, they have saved $45.00

In one week, they have saved $4.50
In x week, they have saved $45.00

We can make a proportion and solve it.

$\frac{1}{4.5} = \frac{x}{45}$

After cross multiplying we get

$4.5x = 45$

Solving for 'x' we get:

x = 10

Mick and Duane have been saving their money for 10 weeks.

Answer 2

The have been saving for 10 weeks.

Given:
Duane = $5 every other week. meaning every 2 weeks
Mick = $2 every week
Amount Saved = $45

First, divide Duane's $5 by 2 to get his weekly contribution.
$5/2 = $2.50

let x be the number of weeks.

Duane + Mick = $45
2.50x + 2x = 45
4.50x = 45
4.50x/4.50 = 45/4.50
x = 10 weeks

to check:
2.50x + 2x = 45
2.50(10) + 2(10) = 45
25 + 20 = 45
45 = 45