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17 votes
17 votes
The length of a rectangular box is 4 times its width, and its height is 6 ft more than its width. The volume of the box is 47 ft3.

find the width of the box. Round your answer to two decimal places.

User Gregg Duncan
by
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1 Answer

26 votes
26 votes

Answer:

1.27

Explanation:

When completing word problems, it's always important to first turn everything into an equation.

The volume of a rectangular box is:


V=lhw

Where l is the length, h is the height, and w is the width.

Which we can write down the equation:


47 ft^3=(4w)(6+w)(w)

Next up, distribute:


47=4w^2(6+w)\\47=24w^2+4w^3\\4w^3+24w^2-47=0

We have a cubic equation, you can solve it using a calculator.

We have three solutions, and they are:


w=-5.62919529..., -1.64201009..., 1.27120539...

Since lengths cannot be negative, there is just one solution:
w=1.27120539...

And rounding it gives:


w=1.27

And don't forget to put ft at the end!

User Brian Underwood
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2.5k points