Begin by determining the ratios of each paint color in one gallon. Then write a system of equations for the cost. Remember that 1 gallon equals 4 quarts.
Cost of Red Paint: $7.75 Cost of Yellow Paint: $5.75
Practice makes perfect
We will first determine the parts of red and yellow in one-gallon of pumpkin orange paint and in one-gallon of pepper red paint. We can write the given information into a table. Then we can write the ratios of red and yellow in the mixed paints correspondingly.
Number of Red Parts in the Ratio
Number of Yellow Parts in the Ratio
Ratio of Red Paint
Ratio of Yellow Paint
2 Gallon of Pumpkin Orange
2
6
2/2+6=2/8
6/2+6=6/8
2 Gallon of Pepper Red
5
3
5/5+3=5/8
3/5+3=3/8
Let's r be the cost of red paint per gallon and y be the cost of yellow paint per gallon. We know that the store sells a gallon of pumpkin orange paint for $25, and sells a gallon of pepper red paint for $28. Next, we will write two equations to represent the costs.
Cost of Red in One Gallon ($)
Cost of Yellow in One Gallon ($)
Total Cost ($)
Equation
Pumpkin Orange
2/8 r=1/4 r
6/8y=3/4y
25
1/4 r+3/4y=25
Pepper Red
5/8 r
3/8y
28
5/8 r+3/8y=28
With these equations we can now create our system.
14r+ 34y=25 58r+ 38y=28
Let's solve the system using the Elimination Method.
Finally, we know the cost of one gallon of each paint. However, we are asked to find cost of one quart of each paint. Since 1 gallon equals 4 quarts, we will divide the cost of each paint by 4 to find the cost of one quart.
