Solve using a system of two equations in two unknowns.
-A vendor sells hot dogs and bags of potato chips. A customer buys 2 hot dogs and 2 bags of potato chips for $3.50. Another customer buys 3 hot dogs and 5 bags of potato chips for $6.75. Find the
Cost of each item.
A) $1.00 for a hot dog; $0.75 for a bag of potato chips
B) $0.75 for a hot dog; $1.00 for a bag of potato chips
C) $1.00 for a hot dog; $1.00 for a bag of potato chips
D) $1.25 for a hot dog; $1.00 for a bag of potato chips

Question

Quizplus · Accepted Answer

Let x be the cost of a hot dog and y be the cost of a bag of potato chips. Then we have the following system of equations:
2x + 2y = 3.5
3x + 5y = 6.75
Multiplying the first equation by 3 and subtracting it from the second equation gives:
x + 7y = 3.75
Solving this equation and the first equation simultaneously, we get:
x = 1
y = 0.75
Therefore, the cost of a hot dog is $1.00 and the cost of a bag of potato chips is $0.75, so the best choice is (A).

Solve Using a System of Two Equations in Two Unknowns