Duane and mick are saving their money to build a treehouse. 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?

They have been saving their money for 10 weeks.

Duane = $5 every two weeks
Mick = $2 every week.

Get the value of Duane's weekly contribution = $5 / 2 = $2.5

Duane's share + Mick's share = $45
$2.5x  + $2.0x = $45   ===>> equation can also be x(2.5 + 2) = 45
$4.5x = $45
$4.5x / $4.5 = $45 / $4.5
x = 10 weeks.

To check:

$2.5(10) + $2(10) = $45
$25 + $20 = $45
$45 = $45

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The answer would be 7 cages