Question

Your making maple syrup. You mix 5 cent and 25 cent maple syrup. You make 128 ounces that cost 18 cents an ounce. You much of each maple syrup ws required?

Answer 1

Suppose you're using C ounces of Cheap and E ounces of Expensive syrup. Then:
C + E = 128
5C + 25E = 18 x 128

Multiply the first equation by 5, and you'll get:
5C + 5E = 5 x 128

so:
(5C + 25E) - (5C + 5E) = 20E = (18-5) x 128 = 13 x 128
so E = 13 x 128 / 20 = 83.2
so C = 128 - 83.2 = 44.8

Check it: C costs 5 cents/ounce and E costs 25 cents/ounce, so the total cost is:
(5 x 44.8) + (25 x 83.2) = 2304 cents, and the total amount of syrup is 44.8+83.2=128 ounces, so the cost is 2304 cents divided by 128 ounces = 18 cents per ounce.