A linear equation word problem in one variable

Liz, Kyle, and Sarah collected empty cans for a recycling drive. Kyle collected 12 more cans than Liz. Sarah collected 2 times as many cans as Liz. If the total number of cans collected was 124, how many cans did Kyle collect?

Solution

Let x be the amount Liz collected

Kyle collected 12 more than Liz or x + 12

Sarah collected 2 times as many as Liz or 2x

Liz's amount + Kyle's amount + Sarah's amount = 124

x + x + 12 + 2x = 124

2x + 12 + 2x = 124

4x + 12 = 124

4x + 12 - 12 = 124 - 12

4x + 0 = 112

4x = 112

4x/4 = 112/4

x = 28

So Liz collected 28.

Kyle collected 28 + 12 = 40 cans

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