How do you solve this problem?

Question

1. A candy factory needs a box with a volume of 420 cubic inches. The height should be 2 inches less than the width and the length is 5 inches greater than the width. What are the dimensions of the box?

If w represents the measurements of the width, which of the following mathematical model satisfy the condition of the above problem?

A. (w-2)(w+5)(w) = 420 B. (w+2)(w-5)(w) = 420

C. (w+2)(w+5)(w) = 420 D. (w-2)(w-5)(w) = 420

2. How wide is the box?

A. 3 inches B. 5 inches C. 7 inches D. 9 inches

3. How high is the box?

A. 5 inches B. 6 inches C. 7 inches D. 8 inches

4. How long is the box?

A. 12 inches B. 14 inches C. 16 inches D. 18 inches

5. What are the dimensions of the box? (Follow V = LWH)

A. 15 in by 12 in by 5 in B. 18 in by 8 in by 12 in

C. 12 in by 3 in by 7 in D. 12 in by 7 in by 5 in

Answer 1

Hi Meg,

If we use the variable, w , to represent the width of the box, then the height would be (w - 2). the length would be (w + 5).

1.The correct choice for the volume would then be letter A:

If w represents the measurements of the width, which of the following mathematical model satisfy the condition of the above problem?

A. (w-2)(w+5)(w) = 420

2. The box would have to be 7 inches wide in order to have the correct measurements for a volume of 420. This is choice C. The height would be 7 -2 = 5 inches; the length would be 7 + 5 = 12 inches, the width would be 7 inches. 5 • 12 • 7 = 420

How wide is the box?

C. 7 inches

3. The box would be 5 inches in height. This is choice A.

How high is the box?

A. 5 inches

4. The box would be 12 inches long. This would be choice A.

How long is the box?

A. 12 inches

5. The correct choice would then be choice D for the dimensions of the box.

What are the dimensions of the box? (Follow V = LWH)

D. 12 in by 7 in by 5 in