Mr. and Mrs. Samson are planning to build a fence around their garden. They are comparing the different measurements for their plans.
Plan A:
1.Posts are 4 ¼ feet in length
2. Post must be installed 7/8 feet below ground level.
Plan B:
1. Posts are 6 ¾ feet in length.
2. Posts must be installed 1 ½ feet below ground level.

1.What will be the height of the fence in plan A?

2. What will be the height of the fence in plan B?

3. Which fence will be taller and by how much?

4. Which plan would you recommend and why?

5. Mr. And Mrs. Samson decide to go with plan A and purchase the materials. Their total bill is $356.88. If they pay $220 in cash and charge the remainder, how much did they charge?

The relationship between the heights of the fence, the lengths, the distance below the ground level is an illustration of addition and subtraction.

The height of the fence is [tex]3\frac 38[/tex] in plan A and [tex]4\frac 34[/tex] in plan B

The fence in plan B is taller by [tex]2\frac{3}{4}[/tex] feet.

The fence in plan B is recommended because: It is taller than the fence in plan A, and it goes below the ground level than plan A
They charge $136.88

Plan A

[tex]Length = 4\frac 14[/tex]

[tex]Ground\ Level = \frac 78[/tex]

Plan B

[tex]Length = 6\frac 34[/tex]

[tex]Ground\ Level = 1\frac 12[/tex]

The height of the fence is calculated by subtracting the length below ground level from the length of the fence. So, we have:

[tex]Plan\ A = 4\frac 14 - \frac 78[/tex] [tex]Plan\ B = 6\frac 34 - 1\frac 12[/tex]

[tex]Plan\ A = \frac{17}{4} - \frac 78[/tex] [tex]Plan\ B = \frac{25}{4} - \frac 32[/tex]

Take LCM

[tex]Plan\ A = \frac{17\times 2 - 7}{8}[/tex] [tex]Plan\ B = \frac{25 - 3\times 2}{4}[/tex]

[tex]Plan\ A = \frac{34 - 7}{8}[/tex] [tex]Plan\ B = \frac{25-6}{4}[/tex]

[tex]Plan\ A = \frac{27}{8}[/tex] [tex]Plan\ B = \frac{19}{4}[/tex]

[tex]Plan\ A = 3\frac{3}{8}[/tex] [tex]Plan\ B = 4\frac{3}{4}[/tex]

Hence, the height of fence is [tex]3\frac 38[/tex] in plan A and [tex]4\frac 34[/tex] in plan B

The fence in plan B is taller because [tex]4\frac 34[/tex] is greater than [tex]3\frac 38[/tex]

The difference (d) in the heights is:

[tex]d = 4\frac 34 - 3\frac 38[/tex]

[tex]d = \frac{19}{4} - \frac{27}{8}[/tex]

Take LCM

[tex]d = \frac{19 \times 2 - 27}{4}[/tex]

[tex]d = \frac{38 - 27}{4}[/tex]

[tex]d = \frac{11}{4}[/tex]

[tex]d = 2\frac{3}{4}[/tex]

Fence in plan B is taller by [tex]2\frac{3}{4}[/tex] feet.

I will recommend the fence in plan B because:

It is taller than the fence in plan A
It goes below the ground level than plan A

For (5), we have:

[tex]Total = \$356.88[/tex]

[tex]Cash = \$220[/tex]

The remainder is the difference in the total amount and the amount they paid:

[tex]Charge = Total - Cash[/tex]

[tex]Charge = \$356.88 - \$220[/tex]

[tex]Charge = \$136.88[/tex]

Hence, they charge $136.88

Read more about addition and subtraction at:

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