Cartridge Box.
The height of a box containing the HP Laser Jet III printer cartridge is 4 in. more that the width and the length is 1 in. more than the width. If the volume of the box is 630 in. cubed, then what are the dimensions of the box?
630^3=LxWxH
630^3=(1+w)(w)(4+w)
please show me the solutions..and answer..thanks..
Your setup is off a little. The 630 shouldn't be cubed. The cubic just refers to the units, not the number.
So we are solving 630 = (1+w)(w)(4+w)
Distribute with the first two sets of parentheses:
630 = (w + w^2)(4 +w)
Collect like terms and put in descending order:
630 = w^3 + 5w^2 +4w
Now get everything on one side:
0 = w^3 + 5w^2 + 4w - 630
Since you didn't tell me what level of math this is or what technology you can use, I'll assume you can use a solving calculator (like a TI-83). If you graph the w^3 equation we found, its only x-intercept (also known as a zero or root) is approximately x = 7.062881
This is a rounded answer, so if you put it back into our original equation of 630=(w+1)(w)(w+4)
you get: (8.0628821)(7.0628821)(11.0628821) which is pretty close to 630.
Thus, the answer is 8.0628821 in by 7.0628821 in by 11.0628821 in.
I hoped this helped.
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August 23rd, 2009
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