Solve Problems Using Systems in Three Variables
-A vendor sells hot dogs, bags of potato chips, and soft drinks. A customer buys 2 hot dogs, 5 bags of potato chips, and 2 soft drinks for $\$ 10.75$. The price of a hot dog is $\$ 1.25$ more than the price of a bag of potato chips. The cost of a soft drink is $\$ 2.50$ less than the price of two hot dogs. Find the cost of each item.
A) $\$ 2.00$ for a hot dog; $\$ 0.75$ for a bag of potato chips; $\$ 1.50$ for a soft drink
B) $\$ 0.75$ for a hot dog; $\$ 2.00$ for a bag of potato chips; $\$ 1.50$ for a soft drink
C) $\$ 2.00$ for a hot dog; $\$ 1.50$ for a bag of potato chips; $\$ 0.75$ for a soft drink
D) $\$ 2.25$ for a hot dog; $\$ 1.00$ for a bag of potato chips; $\$ 1.50$ for a soft drink

Question

Quizplus · Accepted Answer

Let $h$, $p$, and $s$ represent the cost of a hot dog, a bag of potato chips, and a soft drink, respectively. The given information leads to the following system of equations:1. $2h + 5p + 2s = 10.75$ (from the customer's purchase)2. $h = p + 1.25$ (a hot dog costs $1.25 more than a bag of potato chips)3. $s = 2h - 2.50$ (a soft drink costs $2.50 less than two hot dogs)Solving this system, we find that $h = \$2.00$, $p = \$0.75$, and $s = \$1.50$, which matches choice A.

Solve Problems Using Systems in Three Variables -A Vendor Sells $10.75\$ 10.75$10.75

Solve Problems Using Systems in Three Variables
-A Vendor Sells $\$ 10.75$