Mya has a raised garden bed in the shape of a rectangular prism. the bed is 8 feet long, 3 2/3 feet wide, and 2 feet high. part a: belinda wants to make a raised garden bed that covers the same area as mya’s, but the space she has is only 3 feet wide. how long should her garden bed be? part b: find the volume of mya’s gardening bed. suppose belinda’s garden bed is the same height as mya’s. will belinda’s bed have the same volume? explain. part c: a small bag of soil contains 2 cubic feet. how many bags of soil should mya buy if she wants to fill her garden bed completely? show your work. part d: belinda already has 22 bags of soil. use your answer to part c to find the depth to which she can fill her garden bed

Part A:  The area of Mya's garden would be found by multiplying the length,8, by the width, 3 2/3.  This gives an area of 88/3 or 29 1/3 square feet.  We can set up our equation A = lw to find the length of Belinda's garden.

Divide both sides by 3:
88/3 ÷ 3 = 3x ÷ 3
88/3 * 1/3 = x (remember that when dividing fractions you flip the second one, 3/1, and multiply)
88/9 = x
Belinda's garden would need to be 88/9, or 9 7/9, feet long to have the same area as Mya's.
Part B)
The volume of Mya's garden is found by multiplying length by width by height.  Another way of looking at this is the area of the base multiplied by the height.
8(3 2/3)(2) = (8/1)(11/3)(2/1) = 176/3 = 58 2/3 cubic feet.  
The volume of Belinda's garden would still be the area of the base multiplied by the height; since the area of her garden is the same as the area of Mya's garden, as well as the heights being the same, then yes, hers would have the same volume:
(9 7/9)(3)(2) = (88/9)(3/1)(2/1) = 528/9 = 58 2/3
Part C)
We divide the volume of Mya's bed, 58 2/3 cubic feet, by 2 to find out how many bags:
(58 2/3) ÷ 2 = (176/3) ÷ (2/1) = (176/3) * (1/2) = 176/6 = 29 1/3 bag.  We can't purchase 1/3 of a bag so she will need to purchase 30 bags.
If Belinda has purchased 22 bags, that is 44 cubic feet of soil.  We divide this volume of soil by the area of her bed to find the height it will reach:
44 ÷ (88/3) = (44/1) ÷ (88/3) = (44/1) * (3/88) = 132/88 = 1 1/2 feet.