A group of seven people went to an amusement park and spent $234 on tickets. If a child's ticket costs $28 each and an adult ticket costs $37.50 each, how many
adult tickets and how many child tickets were purchased?

3 adult tickets and 4 child tickets were bought.

4 adult tickets and 3 child tickets

Step-by-step explanation:

So doing 234/7 gives you 33.428... which means its not all just children or adults. (I know that's common sense but it's best to do this anyway to further justify your answer)

The total cost for all 7 people shows that there must be an even amount of adult tickets to end up with a whole number so either 2, 4, or 6 adults.

2 adults = $75

4 adults = $150

6 adults = $225

Now we can use these possibilities to figure out if the left over child tickets added to the adult tickets would equal $234. (quick note: I am using # to show that it doesn't equal $234)

If 2 adults = $75, 5 children = $140, $140+$75 = $215 # $234

If 4 adults = £150, 3 children = $84, $84+$150 = $234

Now because we have already figured out that it would be 4 adult tickets and 3 child tickets, we wouldn't need to figure out 6 adult tickets and 1 child ticket, but, again, this would justify your answer and help to secure your marks.

If 6 adults = $225, 1 child = 28, $28+$225 = $253 # $234

I hope this answer helped you out and if you have any questions I'd be happy to help :)

you need a common difference between consecutive terms to be constant, like 1,2,3,4 or 2,4,6,8, or 1,3,6,9