Question

A food company originally sells cereal in boxes with dimensions 25 cm by 14 cm by 10 cm. To make more profit, the company decreases each dimension of the box by x centimeters but keeps the price the same. If the new volume is 2,208 cm3 by how much was each dimension decreased

Answer 1

Answer:

1.75 cm

Step-by-step explanation:

We are given that the dimensions of the box as 25 cm by 14 cm by 10 cm.

Now, to increase the profit, the dimensions of the box by 'x' cm.

Thus, the new dimensions are (25-x) cm by (14-x) cm by (10-x) cm.

Further, it is given that the volume of the new box is 2,208 $cm^{3}$

As, Volume of the box = Length × Breadth × Height

i.e. 2208 = (25-x) × (14-x) × (10-x)

i.e. $2208 = (25-x) \times (140-24x-x^{2})$

i.e. $2208=x^{3}-x^{2}-740x+3500$

i.e. $x^{3}-x^{2}-740x+1292=0$

On solving this cubic equations, we get that, the solutions are x = 27.6, x = 1.75 and x = 26.8.

Since, the dimensions 25 cm by 14 cm by 10 cm are reduced by x cm.

Thus, if x = 27.6 or x = 26.8, then (10-x) = -17.6 or -16.8, which cannot be possible. So, x = 1.75 cm.

Hence, the dimensions were decreased by 1.75 cm.