Question

A moving van’s cargo area has a maximum volume of 480 cubic feet. Allie is transporting boxes of two sizes: 12 cubic feet and 5 cubic feet. If she wants to carry more than 3 times as many of the smaller boxes, what is the maximum number of larger boxes that she can fit in the van? A) 15 B) 16 C) 17 D) 18

Answer 1

Answer: C) 17

Explanation:

Let x be the number of large boxes

As per given,

Number of small boxes= 3 × (number of large boxes)

i.e. Number of small boxes= 3x

Allie is transporting boxes of two sizes: 12 cubic feet and 5 cubic feet.

Total volume = 12 (number of large boxes) + 5(Number of small boxes)

= 12 x+ 5 (3x)

= 12x+15x

= 27x

A moving van’s cargo area has a maximum volume of 480 cubic feet.

`\Rightarrow\ 27x \leq480`

Divide both sides by 27 , we get

`x\leq17.78`

i.e. maximum value x can take = 17

So, the maximum number of larger boxes that she can fit in the van = 17.

Hence, the correct option is C) 17 .