Question

A cereal manufacturer decides to offer a new family-sized box based on the regular-sized box. They want the volume of the family-sized box to be three times the volume of the regular-sized box. However, they want the length of the family-sized box to be the same as the regular-sized box. If they decide to double the width to create the family-sized box, by what factor must they increase the height?

Answer 1

3/2 or 3 over 2

Explanation:

A cereal manufacturer decides to offer a new family-sized box based on the regular-sized box.

They want the volume of the family-sized box to be three times the volume of the regular-sized box. However, they want the length of the family-sized box to be the same as the regular-sized box.

If they decide to double the width to create the family-sized box, by what factor must they increase the height?

Odyssey Question

Answer 2

volume = l x w x h

to increase volume by 3 you would have 3*l*w*h

so 3*l*w*h= l*2*w* x *h ( x is the scale factor)

cancel out the l w and h on both sides

3 = 2x

Divide both sides by 2

x = 3/2 = 1.5

the height should increase by a factor of 1.5