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Ritchie got a job at the movie theater. On the first day, he sold 5 adult tickets and 7 children tickets for a total of 104. On the second day he sold 7 adult tickets and 3 children tickets for a total of 98. What is the price for each ticket?

Sagot :

Answer:

A = $11; C = $7 tickets

Step-by-step explanation:

Using the given info, we can create a system of equations to find the price of adult and children tickets.

Thus, we have 5A + 7C = 104 and 7A + 3C = 98

The easiest method to solve would be elimination:

sqdancefan

Answer:

  • adult: $11
  • children: $7

Step-by-step explanation:

The sales on the two days can be expressed using equations that can be solved for ticket prices.

Setup

Let x and y represent the prices of adult and children's tickets, respectively. Then the sales revenue for the two days can be expressed in the equations ...

  • 5x +7y = 104
  • 7x +3y = 98

Solution

One of the easiest solution methods is to use a graphing calculator. The first attachment shows the prices are $11 for an adult ticket; $7 for children tickets.

Using the matrix functions of a calculator, the augmented matrix of the equation coefficients can be reduced to row-echelon form. This, too, shows the solution to be (adult price, children price) = ($11, $7). See the second attachment. (The solution is the right-most column of the reduced matrix.)

Yet another solution method can use the coefficients from the equations written in general form:

  • 5x +7y -104 = 0
  • 7x +3y -98 = 0

In this form, we define three products of "cross multiplication":

  Δ1 = (5)(3) -(7)(7) = -34

  Δ2 = (7)(-98) -(3)(-104) = -374

  Δ3 = (-104)(7) -(-98)(5) = -238

Using those, we find the variable values to be ...

  x = Δ2/Δ1 = -374/-34 = 11

  y = Δ3/Δ1 = -238/-34 = 7

(adult price, children price) = ($11, $7)

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You can read more about the cross-multiplication method here:

https://brainly.com/question/26397343

View image sqdancefan
View image sqdancefan
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