Question

Joanie runs the concession stand for the school's 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.

Answer 1

Number of hot dogs sold= 48

Number of Pretzels sold= 33

Explanation:

Let 'h' be the number of hot dogs and 'p' be the number of pretzels that Joanie has sold today.

As it is given that:

Today she sold 15 more hot dogs than pretzels and made $195 in total sales.

i..e in terms of equation it could be represented as:

• h=p+15 which could also be written as:

h-p=15------------(1)

• 2h+3p=195--------(2)

( since Pretzels are $3 each, and hot dogs are $2 each )

Now we solve the two equations above to find the value of h and p.

we will use the method of substitution to solve this system.

Substitute the value of h in terms of p from equation 1 in equation (2) to obtain:

2(p+15)+3p=195

2p+30+3p=195

5p+30=195

5p=195-30

5p=165

p=33.

Now the value of h is:

h=33+15

h=48.

Hence, the number of hot dogs sold by Joanie= 48

and number of Pretzels sold by Joanie= 33

Answer 2

3p+2h=195

p + 15 = h

3p + 2(p + 15) = 195

3p + 2p + 30 = 195

5p = 165 (combine like terms and isolate your variable)

p = 33

33 + 15 = 48 (plug 33 into your original second equation)

ANSWER: 33 pretzels and 48 hotdogs
**You can plug these into your original (first) equation to check your answer