how many adults and how many seniors went to the movie and solve.

Question

The Barnes sisters take their kids to a movie every Wednesday during the summer. Today, they invited their mom and some of her friends to join. They reserved 17 tickets which cost $100. A child’s ticket costs $5, an adult ticket costs $8 and a senior ticket costs $6. The adults outnumber the seniors by 1. Set up a system of equations to determine how many children, how many adults and how many seniors went to the movie and solve.

Answer 1

x = number of child's tickets

y = number of adult tickets

z = number of senior tickets

x + y + z = 17

5x + 8y + 6z = 100

y = z + 1

Eliminate the y's first by arranging the variables on one side and constants on the other.

x + y + z = 17

-y + z = -1

x + 2z = 16

-8x - 8y - 8z = -136

5x + 8y + 6z = 100

-3x - 2z = -36

Eliminate the z's by adding the 2 equations together to find x.

x + 2z = 16

-3x - 2z = -36

-2x = -20

x = 10

Take the value of x and plug it into one of the 2 equations from above to find z.

10 + 2z = 16 → 2z = 6 → z = 3

Take both the values of x and z and plug them into one of the original equations to find y.

10 + y + 3 = 17 → y + 13 = 17 → y = 4

10 children, 4 adults, and 3 seniors went to the movie.