# At a baseball game Gina purchased 6 hotdogs and 3 nachos for $24. Frank purchased 8 hotdogs and 1 nacho for $23. How much is one hotdog and one nacho?

##### 3 Answers

1 Hot dog = $2.50; 1 Nacho = $3.00

#### Explanation:

Let

let

Divide equation 1 by 3

Subtract Equation 3 from Equation 2

Simplifying

1 Hot dog = $2.50

Substitute the value calculated above into Equation 1

1 Nacho = $3.00

See a solution process below:

#### Explanation:

Let's call the price of a hotdog:

Let's call the price of a nacho:

We can then write:

Step 1) Solve the second equation for

Step 2) Substitute

Step 3) Substitute

Hotdogs cost: $2.50

Nachos cost $3.00

Answer:

#### Explanation:

Let

We can set up a system of equations:

We can solve for

Now, we can subtract the first equation from the second equation to cancel out the

Finally, we can find

Therefore the cost of one hotdog and one nacho is