Question

select the correct answer.

joanie runs the concession stand for the schools baseball games. at each game, the best selling items are pretzels and hot dogs. pretzels are \\$3 each, and hot dogs are \\$2 each. today she sold 15 more hot dogs than pretzels and made \\$195 in total sales.

use a system of equations to model the situation above, and determine which of the following are possible amounts of pretzels and hot dogs that joanie sold today.

• 31 pretzels, 51 hot dogs
• 35 pretzels, 45 hot dogs
• 15 pretzels, 30 hot dogs
• 33 pretzels, 48 hot dogs

Explanation:

⚡ Using what you learned: introduction to systems of equations · solving systems by substitution

Step 1: Define variables and set up the system

Let \( p \) be the number of pretzels sold, and \( h \) be the number of hot dogs sold.

Based on the problem description:

1. Pretzels are \( \$3 \) each and hot dogs are \( \$2 \) each, with total sales of \( \$195 \):

$$ 3p + 2h = 195 $$

1. She sold 15 more hot dogs than pretzels:

$$ h = p + 15 $$

Step 2: Solve by substitution

Substitute the expression for \( h \) from the second equation into the first equation:

$$ 3p + 2(p + 15) = 195 $$

$$ 3p + 2p + 30 = 195 $$

$$ 5p + 30 = 195 $$

$$ 5p = 165 $$

$$ p = 33 $$

Step 3: Find the number of hot dogs

Substitute \( p = 33 \) back into the equation for \( h \):

$$ h = 33 + 15 $$

$$ h = 48 $$

Answer:

33 pretzels, 48 hot dogs