SOLUTION: The volume of a 15-oz cereal box is 180.4 in.3. The length of the box is 3.2 in. less than the height, and its width is 2.3 in. Find the height and length of the box to the nearest

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Question 1133295: The volume of a 15-oz cereal box is 180.4 in.3. The length of the box is 3.2 in. less than the height, and its width is 2.3 in. Find the height and length of the box to the nearest tenth.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

given:

V=180.4in%5E3

The length L=h-+3.2in

its width isW=+2.3in

Find the height h and length L+ of the box to the nearest tenth.

V=L%2AW%2Ah ...substitute L and W

L%2AW%2Ah=180.4in%5E3

%28h-+3.2in%292.3in%2Ah=180.4in%5E3

%28h-+3.2in%29%2Ah=180.4in%5E3%2F2.3in

h%5E2-+3.2in%2Ah=78.44in%5E2

h%5E2-+10.6in%2Ah%2B7.4in-78.44in%5E2=0

%28h%5E2-+10.6in%2Ah%29%2B%287.4in%2Ah-78.44in%5E2%29=0

h%28h-+10.6in%29%2B7.4in%28h-10.6in%29=0

%28h+-+10.6in%29+%28h+%2B+7.4in%29+=+0

solutions:

if %28h+-+10.6in%29++=+0 => h=10.6in
if ++%28h+%2B+7.4in%29+=+0=> h=-7.4in=> disregard negative solution

so, the height is 10.6in
go to
L=h-+3.2in plug in h
L=10.6in-+3.2in
L=7.4in

The length is 7.4in