Tickets for a basketball game cost $\backslash (2$ for students and $\backslash )5$ for

adults. The number of students was three less than $10$ times the

number of adults. The total amount of money from ticket sales

was $\$619.$ How many of each ticket were sold?

The number of students was three less than $10$times the number of adults and tickets for a basketball game cost $\$2$for students and $\$5$for adults. The total amount of money from ticket sales was $\$619.$We have to find the number of each ticket sold.

Let xbe the number of adult ticket.

Now, the number of students were three less than $10$times the number of adults.

So, the number of student ticket $10x-3.$

Thus, the table is

The total value of ticket sales is$\$619.$

Write the equation by adding the total value of all the types of coins.

So,$5\left(x\right)+2\left(10x-3\right)=619.$

By proceeding with the equation we get,

$$\begin{gathered} 5\left(x\right)+2\left(10x-3\right)=619 \\ 5x+20x-6=619 \\ 25x=619+6 \\ 25x=625 \\ x=25 \end{gathered}$$

Thus, the number of adult tickets is$25$and the student tickets is$\left[10\left(25\right)-3\right]=247.$

To check the answer replace xby $25$into the original equation.

$$\begin{gathered} 5\left(25\right)+2\left(10\left(25\right)-3\right)=619 \\ 125+2\left(250-3\right)=619 \\ 125+494=619 \\ 619=619 \end{gathered}$$

It is true.

Thus, the number of adult tickets sold is$25$and student ticket sold is$247.$