Respuesta :
Answer:
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.
