Question

A film set designer is using white and colored tiles in a pattern to create paths of different lengths. If x is the length of the path in feet, the number of colored tiles needed to make it is calculated using the rule

(8x2y2)(3xy)

where y represents the number of white tiles.

Which simplified expression represents the number of colored tiles used for a path of length x feet?
• 24x3y3
• 11x3y3
• 24x2y2
• 11x2y2

Answer 1

Answer: First option is correct.

Explanation:

Since we have given that

Let y be the number of white tiles .

Let the x be the length of path in feet.

The number of colored tiles needed to make it is written by

`(8x^2y^2)(3xy)`

We need to simplify the expression:

`(8x^2y^2)(3xy)\\\\=8* 3* x^2* x* y^2* y\ (\because a^m* a^n=a^(m+n))\\\\=24x^3y^3`

Hence, First option is correct.

Answer 2

So this question is asking for the area which needs to be covered with colored tiles. Given the expression above, what we are going to do is to multiply the expressions. So the simplified expression that will represent the number of colored tiles used for a path of length x feet is this:
(8x2y2)(3xy)
24x3y3. So the correct answer would be the first option.
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