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.

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