. Mr. Marcum bought 7 tickets to a puppet show and spent $40. He bought a combination of child tickets for $4 each and adult tickets for $10 each. How many of each ticket did he buy?​

Mr. Marcum bought 5 child tickets and 2 adult tickets.

Step-by-step explanation:

First, assume that Mr. Marcum bought either 7 tickets of child tickets or 7 tickets of adult tickets. I'm using 7 child tickets for this working.

If Mr. Marcum bought 7 child tickets,

total money spent = $4 * 7 = $28

This is not equal to $40 and there has to be more money spent.

We should also calculate the price difference between the adult ticket and the child ticket.

Price difference per ticket = $10 - $4 = $6

This means that if Mr. Marcum bought an adult instead of a child ticket, he would spend $6 more.

In this case, Mr. Marcum has to spend $40- $28 = $12 more.

Hence, the number of adult tickets replacing the child tickets is $12/$6 = 2.

The number of child tickets = 7 - 2 = 5

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