## anonymous one year ago Rachel has a box in the shape of a prism with a square base. The capacity of the box is 150 cubic inches. The height of the box (y) is 112 times the base length of the box (x). Find the approximate height and the length of the box.

1. anonymous

@peachpi

2. anonymous

*1 1/2

3. anonymous

not 112

4. anonymous

|dw:1436190466675:dw|

5. anonymous

The equation you want to solve is \[1.5x^3=150\]

6. anonymous

that isnt any of the answer choices? im confused, the answer options are x = 4 and y = 6 x = 5 and y = 7.5 x = 4.2 and y = 6.3 x = 4.6 and y = 6.9

7. anonymous

i also meant that it isnt 112, it is one and one half

8. anonymous

the volume of a box is all the sides multiplied together. the box has a square base, so two sides are x. It is given in the problem that the height is 1½ * x, that's where 1.5x came from. Multiply the 3 sides lengths together to get the volume is 1.5x³. The volume is also given as 150 in the problem. Therefore, the volume equation is \[1.5x^3=150\] We have to solve this equation for x to get the answer

9. anonymous

We start by moving 1.5 to the other side? How do we do that?

10. anonymous

oooohhh ok ok so i understand how you got the volume, that makes much more sense. and divide it??

11. anonymous

yes

12. anonymous

so i got 100, then what

13. anonymous

Now you have to get rid of the exponent. Since the exponent is 3, take the cube root of both sides

14. anonymous

i got 4.6

15. anonymous

yes

16. anonymous

x = 4.6 then just multiply by 1.5 to get y

17. anonymous

oh so the answer is 6.9

18. anonymous

? so the answer is D?

19. anonymous

yes

20. anonymous

thank you!!!

21. anonymous

you're welcome