A rectangular prism measures 225 inches by 315 inches by 2 inches. How many cubes with edge length 15 inch fit in the prism? Show all work

34 Cubes

Step-by-step explanation:

Step 1: Find the Volume of the Rectangular Prism

The dimensions of the rectangular prism are: 225 inches by 315 inches by 2 inches.

Volume of the Rectangular Prism = 225*315*2=141750 Cubic Inches

Step 2: Find the Volume of the Cube

Edge length of the cube, s=15 Inch

Volume of a Cube =

Volume==3375 Cubic Inches

Step 3: Determine how many cubes fit in the prism

To find out how many cubes fit in the rectangular prism, divide the volume of the rectangular prism by the volume of the cube.

Number of Cubes =Volume of the Rectangular Prism ÷ Volume of Cube

=141750 ÷ 3375

=34

34 Cubes will fit in the rectangular prism.

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step-by-step explanation:

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starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.