X = one pound packages of Value brand.
Y = one pound packages of Superior brand.
75 pounds x 16 ounces per pound = 1200 ounces.
120 pounds x 16 ounces per pound = 1920 ounces.
Value Blend = 4 ounces of A and 12 ounces of B
Superior blend = 8 ounces of A and 8 ounces of B
Grade A = 4x + 8y = 1200 ounces
Grade B = 12x + 8y = 1920 ounces
Solve for X in Grade A equation:
4x + 8y = 1200
Subtract 8y from each side:
4x = 1200-8y
divide all terms by 4:
x = 300 - 2y
Replace X in the 2nd equation with the X above:
12(300-2y) + 8y = 1920
Distribute:
3600 - 24y + 8y = 1920
Combine Y terms:
3600-16y = 1920
Subtract 3600 from each side:
-16y = -1680
Divide both sides by -16:
y = -1680 / -16
y = 105
Replace y with 105 in the last X equation:
x = -2y +300
x = -2(105) + 300
x = -210 + 300
x = 90
90 one pound packages of Value brand
105 one pound packages of Superior brand