Solve using Cramer's Rule.
-Two different gasohol mixtures are available. One contains 5% alcohol and the other 12% alcohol. How much of each should be mixed to obtain 1000 gallons of gasohol containing 10% alcohol?
A) 714 gal 5%, 714 gal 12%
B) 50 gal 5%, 120 gal 12%
C) 417 gal 5%, 583 gal 12%
D) 286 gal 5%, 714 gal 12%

Question

Quizplus · Accepted Answer

To solve this problem using a system of equations, let x be the amount of 5% alcohol mixture and y be the amount of 12% alcohol mixture. The system of equations based on the problem statement is:1. $x + y = 1000$ (The total amount of mixture is 1000 gallons)2. $0.05x + 0.12y = 0.10 \times 1000$ (The total amount of alcohol is 10% of 1000 gallons)Solving these equations simultaneously, we get:From equation 1, $y = 1000 - x$.Substituting $y$ in equation 2 gives:$0.05x + 0.12(1000 - x) = 100$,$0.05x + 120 - 0.12x = 100$,$-0.07x = -20$,$x = 286$.Substituting $x = 286$ into $y = 1000 - x$ gives $y = 714$.Therefore, 286 gallons of the 5% mixture and 714 gallons of the 12% mixture are needed.

Solve Using Cramer's Rule