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? Asingle soft drink?

Answer to Problem 64AYU

Solution:

The price of hot dogis $2.75 and price of so $A$ drink is $1.5.

Explanation of Solution

Given:

One group of people purchased 10 hot dogs and5 soft drinks at a cost of 35.00. A second group bought 7 hot dogs and 4 so f t drinks at a cost of $25.25

Calculation:

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

  $10x+5y=35-\dots 1$

  $7x+4y=25.25\dots -2$

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

  $40x+20y=140\to \dots 3$

  $35x+20y=126.25\dots --4$

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,

  $10x+5y=35$

  $10(2.75)+5y=35$

  $5y=7.5$

  $y=1.5$

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