An elementary school buys tickets for a field trip

[Guest]

An elementary school buys tickets for a field trip to the zoo. The number of children going on the field trip is 8 times the number of adults. Tickets for children cost $4 each and tickets for adults cost \$10 each. The total cost of all of the tickets is \$2862, how many tickets of each type did the school purchase? Please set up and solve this problem following the steps below:


a) Define the unknown quantities in terms of one variable.
b) Translate the question into an equation.
c) Solve the equation, showing all work.
d) Write a complete answer to the question asked, including appropriate units.

[Guest]

Something does not add up in this question..?????

Consider as groups of 8 children + 1 adult = 9. Tickets for each group cost (8 x 4) + (1 x 10) = 32 + 10 = 42

Divide 2862 by 42 gives 68 groups with $6 left over.

68 x 42 = $2856 = cost of all tickets

adult tickets cost 68 x 10 = $680

$2856 - $680 = $2176 cost childrens.

$2176 / 4 = 544 childrens tickets

So 68 adult tickets and 544 childrens tickets

[Guest]

I think you either wrote the question wrong or the person who came up with the question didn't choose the numbers very carefully, because the answer comes out as
[tex]68 \tfrac{1}{7}[/tex] adults and [tex]545 \tfrac{1}{7}[/tex] children

Hope this helped,

R. Baber.

[Guest]

Is my solution not more realistic.....?????

68 adults each with 8 children means 544 children and $6 left over

[Guest]

I agree your solution is more realistic. I'm just saying if you don't violate the fact that "The total cost of all of the tickets is $2862" you end up with fractions of people which is obviously nonsense.

There are variations of this question online (just type "An elementary school buys tickets for a field trip to the zoo" with the quotes into google). All of these variations, however, give integer solutions.

R. Baber.