Question

Wanda is a rectangular cake designer with a specialty in silk screen photo cakes. For every cake that she makes, the width of the cake is 4 inches more than the width of the photo in the middle of the cake, and the length of the cake is 3 times the width of the cake. If x represents the width of the photo, which of the following functions represents the area of the cake? A. c(x) = 3x2 + 24x + 48 B. c(x) = 3x2 + 15x + 16 C. c(x) = 3x2 + 48 D. c(x) = 3x2 + 12

Answer 1

Answer: Option A.

Step-by-step explanation:

Based on the information given in the problem, you can draw the figure shown attached.

The area of  rectangle can be calculated with the following formula:

$A=l*w$

Where l is the length and w is the width.

As you can see in the figure:

- The width is: $x+4$

-The length is: $3(x+4)=3x+12$

Therefore, you must multiply both expressions to obtain the area:

$(x+4)(3x+12)=3x^2+12x+12x+48$

Add like terms:

$3x^2+24x+48$

Then, the function that represents the area of the cake is:

$c(x)=3x^2+24x+48$