Question

A square vegetable garden is to be tilled and then enclosed with a fence. If the fence costs $2.50 per foot and the cost of preparing the soil is $0.40 per ft2, determine the size of the garden that can be enclosed for $140.00.

Answer 1

As usual in algebra, we need to select a variable.
The garden is to be square.
Let x be the length of the side.

Answer 2

Ok, so far?

Answer 3

yes

Answer 4

Now we have fencing that goes all around. That means we need the perimeter. What is the perimeter of a square with side length x?

Answer 5

4 times x

Answer 6

Great.

Answer 7

There will be 4x feet of fence length.
The fence costs $2.50 per foot.
How much will 4x feet of fence cost?

Answer 8

do I take 2.50/4

Answer 9

No.
Look at this:
1 foot cost 1 * $2.50
2 feet cost 2 * $2.50
3 feet cost 3 * $2.50

Answer 10

Then 4x feet cost 4x * 2.50

Answer 11

4x * 2.5 = 10x
4x feet of fencing cost 10x

Answer 12

You multiply the perimeter by the cost per foot, not divide.
Ok?

Answer 13

so 1.6 for soil

Answer 14

Not yet.

Answer 15

Now for the soil preparation, we are given a cost per square foot.
Square foot suggests an area.
Now we need to find the area of our garden.

Answer 16

What is the area of a square with side length x?

Answer 17

x^2

Answer 18

Good.
Since preparing the soil costs $0.40 per square foot,
how much does it cost to prepare x^2 sq ft of soil?

Answer 19

Since you have an area and a price as a rate per square foot, you multiply them together to find the cost.

Answer 20

.40x^2

Answer 21

Good.
Now we have the cost of the fence is 10x, and the cost of the preparation of the soil is 0.4x^2.
We add the two costs together and set it equal to 140. Then solve the equation for x.