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.
[tex]\frac{88}{3}=x*3[/tex]
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.
