Question

an elementary school buys tickets for a field trip to the zoo. the number of children is 8 times the number of adults. tickets cost $8.50 each for Children and tickets for adults cost $19.50 each. if the total cost of all the ticckets is $1827, how many tickets of each type did the school purchase? please define the unknow quantities in terms of one variable then translate into an equation, solve the equation.

Answer 1

The first thing we must do for this case is to define variables.
We have then:
x: tickets for children
y: tickets for adults
We write the system of equations:

`x = 8y 8.50x + 19.50y = 1827`
Solving the system we have:

`8.50 (8y) + 19.50y = 1827 68y + 19.5y = 1827 87.5y = 1827 y = 1827 / 87.5 y = 20.88`
Then, for x we have:

`x = 8y x = 8 * (20.88) x = 167.04`
Answer:
tickets for children: 167
tickets for adults: 21