Posted by jessica on Wednesday, October 1, 2008 at 9:16pm.
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?

math  David Q, Saturday, October 4, 2008 at 3:22pm
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 = (185) 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.