Question

A certain 3​-ft by 3​-ft rubber​ shop-floor mat costs ​$43. A 3​-ft by 4​-ft foam mat costs ​$27. Which of these mats has the lower cost per square​ foot, and how much lower is​ it?

Answer 1

Explanation:

A certain 3​-ft by 3​-ft rubber​ shop-floor mat costs ​$43. Since both sides of the mat are equal, it means that the mat is a square. Area of a square is expressed as Length^2.

The length of the 3​-ft by 3​-ft is

3^2 = 9ft^2

If 9ft^2 cost 43

Then 1ft^2 costs $

x = 43/9 = $4.78 per square foot

A 3​-ft by 4​-ft foam mat costs ​$27

Since both sides of the foam mat are unequal, it means that the foam mat is a rectangle . Area of a rectangle is expressed as Length × width

The length is 4​-ft and the width is

3​-ft

Area of the foam mat = 4×3 = 12 ft^2

If 12ft^2 cost 27

Then 1ft^2 costs $y

y = 27/12 = $2.25 per square foot

The foam mat is cheaper because it has a lower cost per square foot

Difference in cost is $4.78 - 2.25

= $2.53