Question

Rufus collected 18 pounds of aluminum cans to recycle. He plans to collect an additional 2 pounds each week. He wants to collect a total of 42 pounds of aluminum cans. Let x represent the number of weeks Rufus collects aluminum cans.

Answer 1

Answer:

12 weeks

Step-by-step explanation:

Given

$Base\ Value = 18$

$Additional = 2$ weekly

$Maximum = 42$

Required

Determine the number of weeks

Represent the maximum number of pounds with y and the number of weeks with x.

Such that

$y = 42$

From the given parameters, the relationship between y and x is as follows:

$y = base\ value + 2 * x$

Substitute 42 for y and 18 for base value

$42 = 18 + 2 * x$

$42 = 18 + 2x$

Subtract 18 from both sides.

$42 - 18 = 18 - 18 + 2x$

$42 - 18 = 2x$

$24 = 2x$

Divide both sides by 2

$\½ * 24 = 2x * \½$

$12 = x$

$x = 12$

Hence, the number of weeks is 12