Question

How many tickets did Anna purchase for adult tickets And how many did Anna purchased for children’s tickets

Answer 1

children ticket:47

Adult ticket :13

Step-by-step explanation

Step 1

set the equations

Let x represents the number of children's ticket

let y represent the number of adult tickets,

cost of a children ticket: $ 11

cost of a adult ticket: $ 17

so

a)she purchased 60 tickets, so

hence

`x+y=60\Rightarrow equation(1)`

B)she spent a total fo $738, hence

`11x+17y=738\Rightarrow equation(2)`

Step 2

Solve the equations

a) isolate the x value in equation (1) and replace in equation (2)

`\begin{gathered} x+y=60\Rightarrow equation(1) \\ subtract\text{ y in both sides} \\ x+y-y=60-y \\ x=60-y \end{gathered}`

now,replace in equation(2)

`\begin{gathered} 11x+17y=738\Rightarrow equation(2) \\ 11(60-y)+17y=738 \\ 660-11y+17y=738 \\ 6y+660=738 \\ \text{subtract 660 in boht sides} \\ 6y+660-660=738-660 \\ 6y=78 \\ \text{divide both sides by 6} \\ (6y)/(6)=(78)/(6) \\ y=13 \end{gathered}`

therefore,

the number of adult tickets is 13

b)now, replace the y value in equation (1) and solve for x

`\begin{gathered} x+y=60\Rightarrow equation(1) \\ \text{replace} \\ x+13=60 \\ \text{subtract 13 in both sides} \\ x+13-13=60-13 \\ x=47 \end{gathered}`

therefore,

the number of children ticket 47

I hope this helps you