Question

A hardware store mixes paints in a ratio of three parts blue to five parts red to make two gallons of cabbage red . A ratio of seven parts blue to one part red makes two gallons of eggplant purple . A gallon of cabbage red sells for ​$22 ​, and a gallon of eggplant purple sells for ​$26 . Find the cost of 1 quart of blue paint and the cost of 1 quart of red paint.

Answer 1

3b+5r=2 gallons of cabbage red
1r+7b=2gallons of egplant

1 gallon of cabbage sells for 22 (means 2 gallos is 44)
1 gallon of egplant is 26 (means 2 gallons is 52)

3b+5r=44
r+7b=52

r+7b=52
miinus 7b from both sides
r=52-7b
sub 52-7b for r in othe equestion
3b+5(52-7b)=44
3b+260-35b=44
-32b+260=44
minus 260 from both sides
-32b=-216
divide both sides by -32
b=6.75

r=52-7b
r=52-7(6.75)
r=52-47.25
r=4.75


3blue+5r=2gallons
5+3=8
8units=2gallons
 4units=1gallon
1unit=1quart

therefor

1 quart of blue paint is $6.75
1 quart of red paint is $4.75