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This is our project.

This is our project. Jacob builds a wooden box. The box is (x)inches high. The width of the box is 3inches more than the height, and the length is 2inches less than the height. The volume of the box is 3 times the width. What we need to find:.

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This is our project.

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  1. This is our project.

  2. Jacob builds a wooden box. The box is (x)inches high. The width of the box is 3inches more than the height, and the length is 2inches less than the height. The volume of the box is 3 times the width.

  3. What we need to find:

  4. 1.Solve for (x)2.Write an expression for the volume of the box

  5. If V=lwh, then V=(x)(x+3)(x-2) and if V=3(x+3) then 3(x+3) =(x)(x+3)(x-2)

  6. Solving the problem step by step

  7. Step 1: 3(x+3)=(x)(x+3)(x-2) First I removed like terms which was (x+3). 3=(x)(x-2)

  8. Step 2: 3=(x)(x-2) Then I foiled the (x) and (x-2) Giving me 3=x^2-2x

  9. Step 3: 3=x^2-2x Then I subtracted 3 from each side getting X^2-2x-3=0

  10. Step 4: x^2-2x-3=0 I factored the polynomial and got (x-3)(x+1)=0 And I solved for x. (x-3)=0 (x-1)=0 Which makes x=3 and x=1

  11. Step 5: X=3 And the volume of the box is 3(x+3)=(x)(x+3)(x-2) Plug in 3 for x and lets see what we get.

  12. Solve and Check 3(x+3)=(x)(x+3)(x-2) 3(3+3)=(3)(3+3)(3-2) 3(6)=3(6)(1) 18=18 Which makes the solution correct and this means the volume of the box is 18.

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