Solve the problem using two linear equations in two variables and 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 750 gal of gasohol containing 10% alcohol? (Round to the nearest whole gallon.)
A) 536 gal 5%, 536 gal 12%
B) 214 gal 5%, 536 gal 12%
C) 313 gal 5%, 438 gal 12%
D) 38 gal 5%, 90 gal 12%

Question

Quizplus · Accepted Answer

Let x be the amount of 5% alcohol mixture and y be the amount of 12% alcohol mixture. The system of equations is:1) $x + y = 750$ (total mixture)2) $0.05x + 0.12y = 0.10 \times 750$ (alcohol content)Solving this system using Cramer's rule or substitution/elimination methods gives $x = 214$ and $y = 536$.

Solve the Problem Using Two Linear Equations in Two Variables