Question

Melissa wants to make a table representing the area of her vegetable garden for a variety of different lengths of the tomato patch. She uses her area expression to create the table.
Complete the table by typing the correct answer in each box. Use numerals instead of words. Do not round your decimal answers.

Answer 1

Answer:

$\begin{array}{cc}Length \ of \ Tomato \ Patch \ (in \ feet)&Area \ of \ Vegetable \ Garden \ (in \ square \ feet)\\\ [6.25]&338\\6.5&[242.625]\\ \ [6.75]&147.25\\7&[51.875]\end{array}$

Step-by-step explanation:

The date from the given table, is expressed as follows;

Area of Vegetable Garden (in square feet); 338, ___, 147.25, ___

Length of Tomato Patch (in feet); ___, 6.5, ___, 7

The length of the tomato patch increases with decrease in the area of the garden

Given that the length of the tomato patch is the independent variable, we can have;

Length of Tomato Patch (in feet); 6.25, 6.5, 6.75, 7

Therefore, for an increase in the length of the tomato patch from 6.25 to 6.75, (a change of Δl = 0.5) the area of the vegetable garden decreased from 338 to 147.25 which is a decrease of ΔA = 190.75

Therefore, the width of the tomato patch, w = ΔA/Δl = 190.75/0.5 = 381.5

The width of the tomato patch, w = 381.5 ft.

The relationship between the total area, TA, the area of the vegetable garden, A, and the length of the tomato patch, l, is therefore, given as follows;

A = TA - 381.5·l

338 = TA - 381.5×6.25

TA = 338 + 381.5×6.25 = 2,722.375

Therefore, when l = 6.5, we get

A = 2,722.375 - 381.5×6.5 = 242.625

When l = 7, we get

A = 2,722.375 - 381.5×7 = 51.875

Therefore, we get;

$\begin{array}{cc}Length \ of \ Tomato \ Patch \ (in \ feet)&Area \ of \ Vegetable \ Garden \ (in \ square \ feet)\\\ [6.25]&338\\6.5&[242.625]\\ \ [6.75]&147.25\\7&[51.875]\end{array}$