Question

2. A school club sold children's and adults' tickets to a fundraiser. Children's tickets sold for $3.50 each, and adults' tickets sold for $7.50 each. The club sold a total of 62 tickets and collected a total of $365.00. How many children's tickets were sold?A. 19D. 42B. 25C. 37

Answer 1

`B.\text{ }25`

Step-by-step explanation

Let the number of children's tickets be x.

Let the number of adults' tickets be y.

The total number of tickets sold is 62. Therefore, we have that:

`x+y=62`

The total amount collected is $365.00. This implies that:

`3.50x+7.50y=365.00`

Now, we have two simultaneous equations:

`\begin{gathered} x+y=62 \\ 3.50x+7.50y=365.00 \end{gathered}`

From the first equation, make y the subject of the formula:

`y=62-x`

Substitute that into the second equation and solve for x:

`\begin{gathered} 3.50x+7.50(62-x)=365.00 \\ \\ 3.50x+465.00-7.50x=365.00 \\ \\ 3.50x-7.50x=365.00-465.00 \\ \\ -4.00x=-100.00 \\ \\ x=(-100.00)/(-4.00) \\ \\ x=25 \end{gathered}`

Therefore, 25 children's tickets were sold. The correct answer is option B.