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13. A large group of 30 people attended a hockey game. Each person ordered a hotdog or a slice of pizza from the concession stand. Hot dogs cost $2.50 each and a slice of pizza costs $3.25 each. If the total bill for these items was $81.75, how many of each type was purchased?

Respuesta :

semsee45

Answer:

21 hot dogs

9 pizza slices

Step-by-step explanation:

Given information:

  • Group = 30 people
  • Cost of a hot dog = $2.50
  • Cost of a slice of pizza = $3.25
  • Total bill = $81.75

Define the variables:

  • Let x = the number of hot dogs purchased.
  • Let y = the number of pizza slices purchased.

Create two equations from the given information:

[tex]\textsf{Equation 1}: \quad x + y = 30[/tex]

[tex]\textsf{Equation 2}: \quad 2.5x+3.25y=81.75[/tex]

Rewrite Equation 1 to make x the subject:

[tex]\implies x=30-y[/tex]

Substitute this into Equation 2 and solve for x:

[tex]\implies 2.5(30-y)+3.25y=81.75[/tex]

[tex]\implies 75-2.5y+3.25y=81.75[/tex]

[tex]\implies 75+0.75y=81.75[/tex]

[tex]\implies 0.75y=6.75[/tex]

[tex]\implies y=9[/tex]

Substitute the found value of y into the rewritten form of Equation 1 and solve for x:

[tex]\implies x=30-9[/tex]

[tex]\implies x=21[/tex]

Solution

  • Hot dogs purchased = 21
  • Pizza slices purchased = 9

Learn more about systems of equations here:

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rvkacademic

Answer:

Number of hot dogs purchased = 21

Number of pizza slices purchased = 9

Step-by-step explanation:

Let the number of people buying hot dogs be represented by the variable H and the number of people buying pizzas be represented by the variable P

Since H hot dogs were purchased and each hot dog costs $2.50, total amount spent on hot dog purchase = $2.50H

Since P slices of pizza were purchased and each slice of pizza costs $3,25,  total amount spent on hot dog purchase = $3,25P

Total amount spent (in $) = 2.50H + 3.25P and we are given that this total amount is $81.75

So we have an equation in two variables

2.50H + 3.25P = 81.75      (1)

We know the number of people is 30 and that should equal the number of hot dogs and pizza slices purchased

So

H + P = 30     (2)

Multiply Equation (2) on both sides by 2.50
==> 2.50(H + P) = 2.50 x 30

2.50H + 2.50P = 75    (3)

Subtract equation (3) from equation (1) to eliminate the H terms

(1) - (3):

2.50H + 3.25P - (2.50H + 2.50P) = 81.75 -75

2.50H + 3.25P - 2.50H - 2.50P = 6.75

Collect like terms and simplify

==>  (2.50H -2.50H) + (3.25P - 2.50P) = 6.75

==>  0.75P = 6.75

Divide both sides by 0.75

==>  0.75P/0.75 = 6.75/0.75

==>  P = 9

So number of people who bought pizza slices = 9

This is the same as the number of pizza slices that were bought

Substitute for P in Eq (2) H + P = 30
==>  H + 9 = 30

Subtract 9 from both sides

==> H + 9 - 9 = 30 - 9

==>  H = 21

So number of people who bought hot dogs = 21

This is the same as the number of hot dogs purchased

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