Matrices word problem

Question

A hardware store mixes paints in a ratio of to parts blue to six parts yellow to make two gallons of lime green . A ratio of seven parts blue to one part yellow makes two gallons of ocean blue. A gallon of lime green sells for ​$​35, and a gallon of ocen blue sells for ​$30. Find the cost of 1 quart of blue paint and the cost of 1 quart of yellow paint.

Answer 1

For lime green, the ratio is 2 blue: 6 yellow. 2/8 = 1/4B; 6/8 = 3/4Y so in 2 gals of lime green there are 0.5 gal B and 1.5 gal Y. (3:1 ratio)

1 gal of lime green is $35/gal, so 2 gal = $70

For ocean blue, the ratio is 7 blue:1 yellow or 7/8 B to 1/8 Y. In 2 gals of ocean blue there are 1.75 gal B and 0.25 Y. (7:1 ratio)

1 gal of ocean blue is $30/gal, so 2 gal = $60

Now for the system of equations:

Lime green: 0.5B + 1.5Y = 70 → 0.5B + 1.5Y = 70

Ocean blue: (-6)(1.75B + 0.25Y = 60) → -10.5B - 1.5Y = -360

Adding: -10B + 0 = -290 B = $29 for 2 gal or 8 qts. B = 29/8 ≅ $ 3.63/qt

0.5(29) + 1.5Y = 70 → 14.5 + 1.5Y = 70 → 1.5Y = 55.5 Y = $37 for 8 qts or ≅ $4.63/qt

(Hope this is correct - I welcome another analysis/approach if there's an error).

Answer 2

Suppose cost of blue is x,cost of yellow is y

2x+6y=35*2

7x+y=30*2

20x=60*3-35

x=7.25

6y=70-14.5

y=9.25