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.
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: [tex]x = 8y
8.50x + 19.50y = 1827[/tex] Solving the system we have: [tex]8.50 (8y) + 19.50y = 1827
68y + 19.5y = 1827
87.5y = 1827
y = 1827 / 87.5
y = 20.88[/tex] Then, for x we have: [tex]x = 8y
x = 8 * (20.88)
x = 167.04[/tex] Answer: tickets for children: 167 tickets for adults: 21
