A gardener plans to extend the length of a rectangular garden by 7 feet. Let x represent the garden's original length. The expression 9(x+7) represents the area of the garden, where 9 is the width, in feet, and (x+7) represents the extended length, in feet, of the garden. When asked for the area of the extended portion, the gardener incorrectly said it was 16 square feet. Expand the expression to find the area of the extension.

Question

A gardener plans to extend the length of a rectangular garden by 7 feet. Let x represent the​ garden's original length. The expression 9(x+7) represents the area of the​ garden, where 9 is the​ width, in​ feet, and (x+7) represents the extended​ length, in​ feet, of the garden. When asked for the area of the extended​ portion, the gardener incorrectly said it was 16 square feet. Expand the expression to find the area of the extension.

GPT 3.5 · Answer

To expand the expression, we can distribute the 9 to both terms inside the parentheses:

9(x + 7) = 9x + 63.

So, the expression 9(x + 7) represents the area of the garden, which is 9x + 63 square feet.

To find the area of the extension, we can subtract the original area from the extended area:

Area of extended portion = (9x + 63) - x = 8x + 63 square feet.

Therefore, the area of the extension is 8x + 63 square feet.