Chapter 11.1, Problem 64AYU

To determine

To find: One group of people purchased 10 hot dogs and 5 soft drinks at a cost of $\$35.00$. A second group bought 7 hot dogs and 4 soft drinks at a cost of $\$25.25$. What is the cost of a single hot dog? A single soft drink?

Answer to Problem 64AYU

The price of hot dog is $\$2.75$ and price of soft drink is $\$1.5$.

Explanation of Solution

Given:

One group of people purchased 10 hot dogs and 5 soft drinks at a cost of $\$35.00$. A second group bought 7 hot dogs and 4 soft drinks at a cost of $\$25.25$.

Calculation:

Let hotdogs be $x$ and let soft drinks be $y$.

$10x+5y=35$   -----1

$7x+4y=25.25$   -----2

Multiplying 4 on both sides of equation 1 and multiplying 5 on both sides of equation 2 we have.

$40x+20y=140$   -----3

$35x+20y=126.25$   -----4

Subtracting equation 3 from equation 4 we have,

$5x=13.75$

$x=2.75$

Using the value of $x$ to find $y$, using equation 1 we have,

$10x+5y=35$

$10\left(2.75\right)+5y=35$

$5y=7.5$

$y=1.5$

Therefore, the price of hot dog is $\$2.75$ and price of soft drink is $\$1.5$.