Question

If 107 people attend a concert and tickets for adults cost $3.5 while tickets for children cost $1.75 andtotal receipts for the concert was $271.25, how many of each went to the concert?

Answer 1

We have to calculate how many children (C) and adults (A) when to the concert.

We know that the total attendance was 107, so we can write:

`A+C=107`

We also know that the ticket sales were $271.25, which is the sum of the children tickets ($1.75 per child, so a total of 1.75*C) and the adult tickets (3.50*A).

Then, we can write:

`1.75\cdot C+3.50\cdot A=271.25`

We can replace A in the second equation using the information from the first equation as:

`A+C=107\Rightarrow A=107-C`
`\begin{gathered} 1.75C+3.50A=271.25 \\ 1.75C+3.50(107-C)=271.25 \\ 1.75C+374.5-3.50C=271.25 \\ (1.75-3.50)C=271.25-374.5 \\ -1.75C=-103.25 \\ C=(103.25)/(1.75) \\ C=59 \end{gathered}`

Knowing that 59 children attended, we can calculate the number of adults using the first equation:

`\begin{gathered} A=107-C \\ A=107-59 \\ A=48 \end{gathered}`

Answer: To the concert attended 59 children and 48 adults.