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Inequality I'm Stuck Please











































Answer the following question using the five problem solving steps. Be sure to show all of your work.

The volume of a rectangular slab of concrete needs to exceed 72 cu. ft. If the length is 12 feet and the width is 8 feet, how thick does the concrete slab need to be?

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May 01, 2011
Inequality - Solving for Unknown
by: Staff

The question:

Use the five steps for problem solving to answer the following question. Please show all of your work.

The volume of a rectangular slab of concrete needs to exceed 72 cu. ft. If the length is 12 feet and the width is 8 feet, how thick does the concrete slab need to be?


The answer:

The five steps are:

1. Understand what the problem is asking you to do
2. Identify the information provided (known and unknown information)
3. Write (or rewrite) the known and unknown information using mathematical notation (rather than sentences)
4. Solve the problem
5. Check your answer


Applying these 5 steps to your problem:


1. Understand what the problem is asking you to do

(Read the last part of the second sentence in the problem statement.)

How thick does the concrete slab need to be?


2. Identify the information provided (known and unknown information)

Known Information

- volume of a rectangular slab of concrete needs to exceed 72 cu. ft.

- length is 12 ft.

- width is 8 feet.

Unknown Information

- thickness


3. Write (or rewrite) the known and unknown information using mathematical notation (rather than sentences)

V = volume of slab in cubic feet

L = length of slab in feet

W = width of slab in feet

T = thickness of the slab in feet


The formula for the volume of the slab is:

V = L x W x T

The volume of the concrete slab in your problem must be greater than 72 cubic feet:

V > 72

The known measurements are:

L = 12

W = 8


Substitute this known information in the equation for the volume:

Begin with what is known about the volume

V = L x W x T

V > 72

Substitute the L x W x T for the V

L x W x T > 72

Substitute the values of the other known variables (length & width)

12 x 8 x T > 72


4. Solve the equation

Solve for T

12 x 8 x T > 72

96 x T > 72

(96 x T)/96 > 72/96

(96/96) x T > 72/96

1 x T > 3/4

T > 3/4

The final answer is: the thickness of the slab must be greater than ¾ ft (the thickness must be greater than 9 inches)


5. Check the answer

Substitute all values in the original equation:

L x W x T > 72

?T? will actually be any value greater than ¾ foot. However, for this mathematical check, use ¾ for ?T? and an equal sign in the equation.


12 x 8 x (3/4) = 72

96 x (3/4) = 72

72 = 72, correct





Thanks for writing.


Staff
www.solving-math-problems.com



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