how many children tickets were sold and how many adult tickets were sold?

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

Hi,

Let x = the number of children's tickets

Let y = the number of adult tickets

You need not use the entire value of 5.00 or 8.00 due to 5 and 8 being whole numbers.

Therefore:

5x + 8y = 1815

Since you do not know for certain how many tickets of each are sold but do know the total of tickets sold you can use the following equation to express this as:

x + y = 255

Solve for x:

x = 255 - y

Now, substitute the value of 255 - y for x in the previous equation. Therefore:

5x + 8y = 1815

5(255 -y) + 8y = 1815

1275 - 5y + 8y = 1815

3y = 540

y = 180 <---Number of adult tickets sold

x = 255 - 180

x = 75 <----Number of children's tickets sold

Check our work, okay?

5(75) + 8(180) = 1815

375 + 1440 = 1815

Check. I hope this assists you or others and wish you a great day.

Answer 2

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 3

75 children tickets

180 adult tickets

Let x = children

Let y = adult

Rates are $5 for a child and $8 for an adult

Total number of tickets sold is 255

Total revenue collected is 1815 from the rates above

We have one equation for total tickets and one for total revenue as follows:

Equation 1

x + y = 255

Equation 2

5x + 8y = 1815

You can solve by elimination or substitution. I will multiply Equation 1 by negative 5 and use elimination below.

-5(x + y = 255)

-5x - 5y = -1275

Now combine this with Equation 2 eliminates x

-5x - 5y = -1275

5x + 8y = 1815

3y = 540

Divide both sides by 3

y = 180

Substitute 180 for y in original Equation 1 to solve for x

x + 180 = 255

Subtract 180 from both sides

x = 75

Checking in the original equations

Equation 1

75 + 180 = 255

Equation 2

5(75) + 8(180) = 1815

375 + 1440 = 1815