Question

Andrea and Damian are collecting clothing items to donate. When they begin tracking their progress, Damian already has 5 items collected. Damian's goal is to collect 3 items per day, and Andrea's goal is to collect 4 items per day.

Answer 1

5 days

Explanation:

Given

Damian

`Base\ Items = 5`

`Rate = 3` daily

Andrea

`Rate =4` daily

Required [Missing from the question]

How long will they get the same number of items

Represent the number of items with x and the days with y.

So:

For Damian

`y = Base\ Items + Rate * x`

`y = 5 + 3 * x`

`y = 5 + 3 x`

For Andrea

`y = Rate * x`

`y = 4* x`

`y = 4x`

Equate both expressions.

`4x = 5 + 3x`

Collect like terms

`4x - 3x = 5`

`x = 5`

Hence, they will have equal amount of items after 5 days