Answer:
10 ounces
Step-by-step explanation:
The total amount of ounces will the the amount worth 30 cents an ounce (x) plus the 50 ounces worth 20 cents an ounce. This amount is x + 50. The total worth of the mixture should be the worth of the unknown quantity (30 cents an ounce * x ounces) plus the worth of the known quantity (18 cents an ounce * 50 ounces). The total worth is then 30x + 18(50).
Selling the mixture at 20 cents an ounce means the total worth divided by the total amount equals 20 cents per ounce:
[30x + 18(50)] cents / [x + 50] ounces = 20 cents/ounce
Multiplying both sides by (x + 50) ounces yields
(30x + (18)(50) cents = 20(x + 50) cents
which solves to (30x + 900) cents = (20x + 1000) cents
now we use algebra to solve for the value of x
(30x + 900) - 900 = 20x + 1000 - 900 --> 30x = 20x + 100 -->
30x - 20 x --> 20x - 20 x + 100 --> 10x = 100 --> x = 10 ounces
