Question

One adult ticket for a school play cost $10 and one student ticket cost $6. One evening 750 people attended the play and the total receipts were $6860 how many of each type of ticket were sold a full algebraic a solution is required

Answer 1

Given:

Adult ticket cost = $10

Student ticket cost = $6

Total people = 750 people

Total amount = $6860

Find-:

How many of each type of ticket were sold

Explanation-:

Let student is "x."

The adult is "y."

The total people is 750 people,

`\begin{gathered} \text{ Total people }=750\text{ people} \\ \\ x+y=750..............(1) \end{gathered}`

The total amount is $6860

`\begin{gathered} 6x+10y=6860 \\ \\ 3x+5y=3430.................(2) \end{gathered}`

Solve the equation is:

`\begin{gathered} x+y=750 \\ \\ 3x+3y=2250.......................(1)^(\prime) \end{gathered}`

Then eq(2) - eq(1)' then value of "y" is:

`\begin{gathered} 3x+5y-(3x+3y)=3430-2250 \\ \\ 3x+5y-3x-3y=3430-2250 \\ \\ 2y=1180 \\ \\ y=(1180)/(2) \\ \\ y=590 \end{gathered}`

Adult member is 590

Student ticket is:

`\begin{gathered} x+y=750 \\ \\ x+590=750 \\ \\ x=750-590 \\ \\ x=160 \end{gathered}`

The number of students is 160.