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Reil [10]
1 year ago
9

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?
Mathematics
2 answers:
g100num [7]1 year ago
6 0

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.

<h3>Setup</h3>

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

<h3>Solution</h3>

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)

__

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

brainly.com/question/26397343

BigorU [14]1 year ago
3 0

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:

You might be interested in
1) 15^2=4^2+2(32)x<br><br> 2) 105=45+5x
forsale [732]

① 15² = 4² + 2(32) x
225 = 16 + 64x
-64x = 16 - 225
-64x = -209
x = 209/64

② 105 = 45 + 5x
-5x = 45 - 105
-5x = -60
x = 60/5
x = 12

8 0
3 years ago
the basketball court in the park is rectangle two of the sides are 84 feet long and the other two sides are 50 ft long what is t
butalik [34]
Hello!

So, we know that the length of the rectangular basketball court is 84 ft, and the width is 50 ft.

The formula for perimeter of a rectangle is:

P = 2l + 2w

This means that we need to multiply the length by two and the width by two as well.

Substitute:

P = 2(84) + 2(50)

P = 168 + 100

P = 268 ft

ANSWER:

The perimeter of the basketball court is 268 feet long.
6 0
3 years ago
Tasha lists all the multiple of 3 from 3 to99. Tony lists all the multiples of 5 from 5 to100. What is the first number that is
IrinaVladis [17]

Answer:

  • Multiples of 3 = 3, 9
  • Multiples of 5 = 5, 10

Step-by-step explanation:

In a list of 3 to 99, the first multiple of 3 will be none other than 3 itself because when multiplied by 1, you get three.

The second number will be: 3 * 2 = 6

In a list from 5 to 100, the first multiple will be 5 with 5 being a multiple of itself when multiplied by 1.

Second number = 5 * 2 = 10

7 0
3 years ago
Sandy wants to make a punch recipe with 2 parts pineapple juice to 6 parts ginger ale if you wants to increase the recipe using
Blizzard [7]

Answer:

24

Step-by-step explanation:

If you go from 2 parts pineapple to 8, thats a 4x increase. Therefore 6x4=24 (6 from the Ginger)

4 0
3 years ago
Point T is on line segment \overline{SU} SU . Given ST=12ST=12 and TU=3,TU=3, determine the length \overline{SU}. SU
vova2212 [387]

Answer:

SU = 15

Step-by-step explanation:

Given that,

Point T is on line segment SU. So,

SU = ST + TU

Putting all the values, we get :

SU = 12 + 3

SU = 15

Hence, the length of SU is 15 units.

3 0
3 years ago
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