Solve the problem using the elimination method.
-A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato chips for $6.50. Another customer buys 5 hot dogs and 3 bags of potato chips for $14.25. Find the cost of each item.
A)$2.25 for a hot dog; $1.00 for a bag of potato chips
B)$2.50 for a hot dog; $1.25 for a bag of potato chips
C)$1.00 for a hot dog; $2.25 for a bag of potato chips
D)$2.25 for a hot dog; $1.25 for a bag of potato chips

Question

Quizplus · Accepted Answer

Let the cost of a hot dog be $x$ and the cost of a bag of potato chips be $y$. The system of equations based on the given information is:$$2x + 2y = 6.50$$$$5x + 3y = 14.25$$Multiplying the first equation by 1.5 gives:$$3x + 3y = 9.75$$Subtracting the second equation from this result gives:$$-2x = -4.50$$Solving for $x$ gives $x = 2.25$. Substituting $x = 2.25$ into the first equation and solving for $y$ gives $y = 1.00$.

Solve the Problem Using the Elimination Method