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Bumek
17 days ago
7

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.
Mathematics
2 answers:
PIT_PIT [9.1K]17 days ago
6 0
3p+2h=195

p + 15 = h

3p + 2(p + 15) = 195

3p + 2p + 30 = 195

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

p = 33

33 + 15 = 48 (substitute 33 into the original second equation)

SOLUTION: 33 pretzels and 48 hot dogs
**Verify by substituting these values back into the original equation
Leona [9.2K]17 days ago
4 0

Answer:

Number of hot dogs sold= 48

Number of pretzels sold= 33

Step-by-step explanation:

Designate 'h' for the quantity of hot dogs and 'p' for the quantity of pretzels sold today by Joanie.

It is given that:

She sold 15 more hot dogs than pretzels and made $195 overall.

This situation can be articulated as:

  •  h=p+15 which can also be arranged as:

          h-p=15------------(1)  

  • 3h+2p=195--------(2)

(Given that pretzels are priced at $3 each, while hot dogs are $2 each)

Now, we will solve these two equations to determine h and p.

Using substitution, we insert the expression for h from equation 1 into equation 2:

2(p+15)+3p=195

2p+30+3p=195

5p+30=195

5p=195-30

5p=165

Thus, p=33.

Then, for h:

h=33+15

h=48.

Consequently, Joanie sold 48 hot dogs

and 33 pretzels

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