Answer:
Part 1) The units rates are
A) ![0.1165\frac{\$}{oz}](https://tex.z-dn.net/?f=0.1165%5Cfrac%7B%5C%24%7D%7Boz%7D)
B) ![0.1656\frac{\$}{oz}](https://tex.z-dn.net/?f=0.1656%5Cfrac%7B%5C%24%7D%7Boz%7D)
C) ![0.0516\frac{\$}{oz}](https://tex.z-dn.net/?f=0.0516%5Cfrac%7B%5C%24%7D%7Boz%7D)
D) ![0.0579\frac{\$}{oz}](https://tex.z-dn.net/?f=0.0579%5Cfrac%7B%5C%24%7D%7Boz%7D)
Part 2) The best buy is the size 48 1/4 oz
Step-by-step explanation:
we know that
To find out the unit rate divide the total cost by the total volume
Part 1) Calculate the unit rate for each size
case A) we have
8 1/2 ounce bottle costs $0.99
Convert mixed number to an improper fraction
![8\frac{1}{2} =\frac{8*2+1}{2}=\frac{17}{2}\ oz](https://tex.z-dn.net/?f=8%5Cfrac%7B1%7D%7B2%7D%20%3D%5Cfrac%7B8%2A2%2B1%7D%7B2%7D%3D%5Cfrac%7B17%7D%7B2%7D%5C%20oz)
Find the unit rate
![\frac{0.99}{(17/2)}= 0.1165\frac{\$}{oz}](https://tex.z-dn.net/?f=%5Cfrac%7B0.99%7D%7B%2817%2F2%29%7D%3D%200.1165%5Cfrac%7B%5C%24%7D%7Boz%7D)
case B) we have
18 2/2 oz. bottle costs $1.49
Convert mixed number
![18\frac{2}{2} =18+1=19\ oz](https://tex.z-dn.net/?f=18%5Cfrac%7B2%7D%7B2%7D%20%3D18%2B1%3D19%5C%20oz)
Find the unit rate
![\frac{1.49}{19}= 0.1656\frac{\$}{oz}](https://tex.z-dn.net/?f=%5Cfrac%7B1.49%7D%7B19%7D%3D%200.1656%5Cfrac%7B%5C%24%7D%7Boz%7D)
case C) we have
48 1/4 oz. carton costs $2.49
Convert mixed number to an improper fraction
![48\frac{1}{4} =\frac{48*4+1}{4}=\frac{193}{4}\ oz](https://tex.z-dn.net/?f=48%5Cfrac%7B1%7D%7B4%7D%20%3D%5Cfrac%7B48%2A4%2B1%7D%7B4%7D%3D%5Cfrac%7B193%7D%7B4%7D%5C%20oz)
Find the unit rate
![\frac{2.49}{(193/4)}= 0.0516\frac{\$}{oz}](https://tex.z-dn.net/?f=%5Cfrac%7B2.49%7D%7B%28193%2F4%29%7D%3D%200.0516%5Cfrac%7B%5C%24%7D%7Boz%7D)
case D) we have
64 3/4 oz. carton costs $3.75
Convert mixed number to an improper fraction
![64\frac{3}{4} =\frac{64*4+3}{4}=\frac{259}{4}\ oz](https://tex.z-dn.net/?f=64%5Cfrac%7B3%7D%7B4%7D%20%3D%5Cfrac%7B64%2A4%2B3%7D%7B4%7D%3D%5Cfrac%7B259%7D%7B4%7D%5C%20oz)
Find the unit rate
![\frac{3.75}{(259/4)}= 0.0579\frac{\$}{oz}](https://tex.z-dn.net/?f=%5Cfrac%7B3.75%7D%7B%28259%2F4%29%7D%3D%200.0579%5Cfrac%7B%5C%24%7D%7Boz%7D)
Part 2) which size is the best buy
we know that
The best buy is the one with the smallest unit rate
so
![0.0516\frac{\$}{oz}](https://tex.z-dn.net/?f=0.0516%5Cfrac%7B%5C%24%7D%7Boz%7D)
The best buy is the size 48 1/4 oz