A gardener plans to extend the length of a rectangular garden by 6 feet. Let x represent the garden's original length. The expression 7(x+6) represents the area of the garden, where 7 is the width, in feet, and (x+6) represents the extended length, in feet, of the garden. When asked for the area of the extended portion, the gardener incorrectly said it was square13 feet. Expand the expression to find the area of the extension. Then describe an error the gardener might have made.

Question

A gardener plans to extend the length of a rectangular garden by 6 feet. Let x represent the​ garden's original length. The expression 7(x+6) represents the area of the​ garden, where 7 is the​ width, in​ feet, and (x+6) represents the extended​ length, in​ feet, of the garden. When asked for the area of the extended​ portion, the gardener incorrectly said it was  square13 feet. Expand the expression to find the area of the extension. Then describe an error the gardener might have made.

GPT 3.5 · Answer

To expand the expression for the area of the garden's extension, we substitute x+6 into the expression 7(x+6):

Area of the extension = 7(x+6)
= 7x + 42

Now, when the gardener incorrectly said that the area of the extension was 13 square feet, it implies that he equated the expression 7x + 42 with 13, which implies:
7x + 42 = 13

The error the gardener made was incorrectly solving the equation. To solve the equation correctly, we subtract 42 from both sides of the equation:

7x + 42 - 42 = 13 - 42
7x = -29

Then, we divide both sides of the equation by 7 to solve for x:

(7x)/7 = (-29)/7
x = -29/7

So, the gardener made an error in solving the equation, which resulted in the incorrect value of x.