Question

Mindy owns 20 pairs of shoes and every week she purchases two more pairs.And she destroys one. How long will it take for her closet to have 50 pairs of shoes?

Write an equation and solve.

Answer 1

y = x + 20

30 weeks

Explanation:

The given scenario can be modelled using the linear equation:

`y=mx+b`

where:

• m is the rate of change (slope).
• b is the initial value (y-intercept.

Mindy initially owns 20 pairs of shoes. Therefore, the initial value is b = 20.

If Mindy purchases 2 pairs but destroys 1 pair each week, then she is gaining 1 pair of shoes each week. Therefore, the rate of change is m = 1.

Therefore, the equation is:

`y=x+20`

where:

• x is time in weeks.
• y is the number of shoes Mindy owns.

To find how long it will take for Mindy's closet to have 50 pairs of shoes, substitute y = 50 into the equation and solve for x:

`\implies 50=x+20`

`\implies 50-20=x+20-20`

`\implies 30=x`

`\implies x=30`

Therefore, it will take Mindy 30 weeks to have 50 pairs of shoes in her closet.