Q. 64 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

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

Step 1 : Given information

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

Step 2: Write and solve the equation

Let x be the price of  hot dog and y be the price of soft drink

One group of people purchased 10 hot dogs and 5 soft drinks at a cost of $35.00.

Hence $10x+5y=35 \left(1\right)$

A second bought 7 hot dogs and 4 soft drinks at a cost of $25.25 

And $7x+4y=25.25$             (2)

Multiply equation 1 by 4 and multiply equation 2 by 5 And subtract

We get,

$40x+20y=140-35x-20y=-126.255x=13.75$

Hence $x=2.75$

Now we find the value of y

$$\begin{gathered} 10x+5y=35 \\ 10(2.75)+5y=35 \\ y=1.5 \end{gathered}$$

Step 3: Conclusion

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