Chapter 1, Problem 18CR

To determine

To calculate: The number of student, adult and children tickets that have been sold in band concert.

Answer to Problem 18CR

Student tickets $=200$

Adult tickets $=350$

Children tickets $=50$

Explanation of Solution

Given information: Number of people in concert $=$ $600$

Revenue for the concert $=\$3150$

Cost of children tickets $=\$2$

Cost of student tickets $=\$3$

Cost of adult tickets $=\$7$

Formula used: Substitution method

In which we solve for the one variable $x$ or $y$ and then substitute the variable into other equation.

Calculation: For this, firstly we let the number of student tickets are $x$

Let the number of children tickets are $y$

Then the adult tickets are $x+150$

Now, total revenue cost is $600$

  $\Rightarrow$ $x+\left(x+150\right)+y=600$

  $\Rightarrow 2x+y=450$

Now, Money gained from the student tickets $=3x$

Money gained from the adults $=7\left(x+150\right)$

Money gained from the children $=2y$

According to given problem:

  $3x+7\left(x+150\right)+2y=3150$

On solving above equation, we get

  $5x+y=1050$

Taking equations $2x+y=450$ and $5x+y=1050$

Put the value of $y$ from the equation $2x+y=450$ into equation $5x+y=1050$ , we get

(Student tickets) $x=200$

Putting the value of $x$ in equation $2x+y=450$ , we get

(Children tickets) $y=50$

Put the value of $x$ in $x+150$ (Adult tickets), we get

Adult tickets $=350$