A movie theatre charges $6 for children, $8 for adults and $5 for senior citizens. An extended family of 14, decide to go to the movies one weekend. There are twice as many children as senior citizens. The family
spent $84 on tickets.
Complete the following:
x represents
y represents
z represents
4
First equation
+
+
A=
Second equation
AX +
Y+
AZ=
4
Third equation
4X +
4 Y-
A Z=
4
Children tickets
4 Adult tickets
Senior Citizen tickets
1 2 3 4 5 6 7 8 9 10
Next

There are 4 senior citizens, 8 children, and 2 adults in the extended family

Step-by-step explanation:

The amount the movie theater charges for children = $6

The amount the movie theater charges for adult = $8

The amount the movie theater charges for senior citizens = $5

The total number of persons in the extended family = 14

The number of children in the extended family = 2 × The number of senior citizens

The amount the extended family spent on tickets = $84

x represents the number of senior citizens in the extended family

y represents the number of children in the extended family

z represents the number of adults in the extended family

y = 2·x

x + y + z = 14

Substituting the value of y = 2·x in the above equation gives;

x + 2·x + z = 14

z = 24 - (x + 2·x) = 14 - 3·x

z = 14 - 3·x

x × 5 + y × 6 + z × 8 = 84

Substituting the value of x, y, and z in the above equation gives;

x × 5 + 2·x × 6 + (14 - 3·x) × 8 = 84

5·x + 12·x - 24·x + 112 = 84

112 - 84 = 24·x - (5·x + 12·x) = 7·x

7·x = 112 - 84 = 28

x = 28/7 = 4

x = 4

∴ The number of senior citizens = 4

y = 2 × x = 2 × 4 = 8

y = 8

The number of children = 8

z = 14 - 3·x = 14 - 3 × 5 = 2

z = 2

The number of adults = 1

Therefore, there are 4 senior citizens, 8 children, and 2 adults in the extended family.

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step-by-step explanation: