

- <u>While </u><u>shopping </u><u>for </u><u>clothes </u><u>Tracey </u><u>spent </u><u>3</u><u>8</u><u>$</u><u> </u><u>less </u><u>than </u><u>3</u><u> </u><u>times </u><u>of </u><u>what </u><u>Daniel </u><u>spent </u>

- <u>We </u><u>have </u><u>to </u><u>determine </u><u>the </u><u>total </u><u>cost </u><u>spent </u><u>by </u><u>daniel</u>

Cost spent by Tracey for her clothes = 38$
Let assume the spending by Daniel is x





94/100 miles is the answer. I dont know what form you wanted the answer in but yeah.
Let h = height of the box,
x = side length of the base.
Volume of the box is

.
So

Surface area of a box is S = 2(Width • Length + Length • Height + Height • Width).
So surface area of the box is


The surface are is supposed to be the minimum. So we'll need to find the first derivative of the surface area function and set it to zero.

![4x = \frac{460}{ x^{2} } \\ 4x^{3} = 460 \\ x^{3} = 115 \\ x = \sqrt[3]{115} = 4.86](https://tex.z-dn.net/?f=%204x%20%3D%20%5Cfrac%7B460%7D%7B%20x%5E%7B2%7D%20%7D%20%20%5C%5C%20%204x%5E%7B3%7D%20%3D%20460%20%20%5C%5C%20x%5E%7B3%7D%20%3D%20115%20%20%5C%5C%20x%20%3D%20%20%5Csqrt%5B3%5D%7B115%7D%20%3D%204.86%20)
Then

So the box is 4.86 in. wide and 4.87 in. high.
Both solutions are x<span> = 2 and x = -2 are correct
because
</span>when x = 2 , |2| = 2
and
<span>when x = -2, |-2| = 2
hope it helps</span>