# Word problem

• Mar 24th 2006, 04:23 AM
roseh
Word problem
A box (rectangular/no top) is to have a volume of 64 cubic meters. The width of the base must be 4 meter to insert into a vault. When trimmed to size, material cost $12.00 per square meter for the base and$6.00 per square meter for the sides. What is the cost for the box?

Thanks
• Mar 24th 2006, 05:19 AM
CaptainBlack
Quote:

Originally Posted by roseh
A box (rectangular/no top) is to have a volume of 64 cubic meters. The width of the base must be 4 meter to insert into a vault. When trimmed to size, material cost $12.00 per square meter for the base and$6.00 per square meter for the sides. What is the cost for the box?

Thanks

The width of the box is $\displaystyle 4$m, let the height be $\displaystyle h$m and the depth be $\displaystyle d$m.

Then to make the volume $\displaystyle 64 m^3$ we have:

$\displaystyle 4\times h \times d=64$

The area of the base is $\displaystyle 4\times d$ so the cost of the base is:

$\displaystyle 6 \times 4 \times d$

The area of the sides id $\displaystyle (2 \times 4+2\times d)\times h$, so the cost of the sides is:

$\displaystyle 12 \times (2 \times 4+2\times d)\times h =96+24\times d \times h$

but $\displaystyle 4\times h \times d=64$, so the cost of the sides is:

$\displaystyle 96+24\times d \times h=96+6 \times (4 \times d \times h)=\$ 480
$. Hence the total cost is:$\displaystyle
480+24 \times d
\$ dollars

and you don't know enough to simplify further.

RonL