Tickets to a new play at $5.00 for children and $8.00 for adults. If 255 tickets are sold and the revenue from ticket sales is $1815.00,

Question

Tickets to a new play at $5.00 for children and $8.00 for adults. If 255 tickets are sold and the revenue from ticket sales is $1815.00, how many children tickets were sold and how many adult tickets were sold? Make sure you define variables and write out algebraic equations before you solve.

Answer 1

Tickets to a new play cost $5.00 for children and $8.00 for adults. If 255 tickets are sold and the revenue from ticket sales is $1,815, how many children’s tickets were sold and how many adult tickets were sold? Make sure you define the variables and write out algebraic equations before you solve.

Let: Children’s tickets = C

Let: Adult tickets = A

Given: Children ticket prices = $5

Given: Adult ticket prices = $8

Given: Total tickets sold = 255

Given: Total revenue = $1,815

C + A = 255                  (1)

5C + 8A = 1,815           (2)

Multiply equation (1) by -5

-5C - 5A = -1,275

5C + 8A = 1,815

Add the two equations together. The C variables will drop out. That will leave us with A variables only. We then solve for A and substitute and solve for C.

3A = 540

Divide through by 3

A = 180 Adult tickets sold

Now substitute 180 for A and solve for C.

C + A = 255

C + 180 = 255

C = 75 Children’s tickets sold

Check 1

C + A = 255

75 + 180 = 255

255 = 255 Check

Check 2

5C + 8A = 1,815

5 (75) + 8 (180) = 1,815

375 + 1,440 = 1,815

1,815 = 1,815 Check

The final answer is, there were 75 Children’s tickets sold and 180 tickets sold to Adults.

.

Answer 2

let x = number of children's tickets

 

let y = number of adult tickets

 

5x + 8y = 1815

 

x + y = 255

 

y = 255 - x

 

5x + 8(255 - x) = 1815

 

5x + 2040 - 8x = 1815

 

-3x = -225

 

x =75

 

y = 255 - x

 

y = 180

 

75 children's tickets and 180 adult tickets

 

check: 75(5) + 180(8) = 1815