Answer:
<em>The best buy by unit price is the 16-oz can whose unit price is $0.07/oz.</em>
Step-by-step explanation:
The problem speaks of three sizes of cans, 12 oz, 16 oz, and 24 oz.
The prices of the three sizes of the cans are unknown. We are looking for the best unit cost, or dollars per oz.
Let x = unit cost of the 12-oz can.
Let y = unit cost of the 16-oz can.
Let z = unit cost of the 24-oz can.
The cost of the 12-oz can is 12x.
The cost of the 16-oz can is 16y.
The cost of the 24-oz can is 24z.
The 12-oz can costs $0.16 less than the 16-oz can.
12x = 16y - 0.16
The 16-oz can costs $0.68 less than the 24-oz can.
16y = 24z - 0.68
The unit price of the 24-oz can is $0.005 less than the unit price of the 12-oz can.
z = x - 0.005
There are three equations written in bold above. The form a system of equations in three unknowns. Each unknown is a unit price.
Replace z of the second equation with the third equation.
16y = 24(x - 0.005) - 0.68
16y = 24x - 0.12 - 0.68
16y = 24x - 0.8
Subtract 16y from both sides and add 0.8 to both sides. Then switch sides. You get
24x - 16y = 0.8 (Eq. 1)
Now take the original first equation in bold above. Subtract 12x from both sides. Add 0.16 to both sides. Switch sides. You get.
-12x + 16y = 0.16 (Eq. 2)
Add Eq. 1 and Eq. 2 to eliminate y.
12x = 0.96
x = 0.08
The unit price of the 12-oz can is $0.08/oz.
A 12-oz can costs 12x = $0.96.
12x = 16y - 0.16
0.96 = 16y - 0.16
1.12 = 16y
y = 1.12/16 = 0.07
The unit price of the 16-oz can is $0.07/oz.
z = x - 0.005
z = 0.08 - 0.005
z = 0.075
The unit price of the 24-oz can is $0.075/oz.
The unit prices of the 12-oz, 16-oz, and 24-oz cans are $0.08/oz, $0.07/oz, and $0.075/oz, respectively.
The best buy by unit price is the 16-oz can whose unit price is $0.07/oz.
