A family bought a total of 32 adult and child tickets to eat at the dining hall. Adult tickets are $21 each and children are $15 each.

The family paid a total of $282

Write an equation to model the total number of tickets sold.

Write an equation to model the cost of tickets sold.

How many of adult tickets, “x” and child tickets, “y” did they buy?

250 $3 tickets and 100 $2 tickets were sold.

Step-by-step explanation:

Solution:

Step 1: Set up a table with quantity and value.

quantityvaluetotal

$3 tickets  

$2 tickets  

together  

Step 2: Fill in the table with information from the question.

The cost of tickets for a play is $3.00 for adults and $2.00 for children. 350 tickets were sold and $950 was collected. How many tickets of each type were sold?

Let x = number of $3 tickets

Let y = number of $2 tickets

Total = quantity × value

quantityvaluetotal

$3 ticketsx33x

$2 ticketsy22y

together350  950

Step 3: Add down each column to get the equations

x + y = 350                    (equation 1)

3x + 2y = 950                (equation 2)

Use Substitution Method

Isolate variable x in equation 1

x = 350 – y                     (equation 3)

Substitute equation 3 into equation 2

3(350 – y) + 2y = 950

1050 – 3y + 2y = 950

3y – 2y = 1050 – 950

y = 100

Substitute y = 100 into equation 1

x + 100 = 350

x = 250

250 $3 tickets and 100 $2 tickets were sold.

what you just answered

Step-by-step explanation:

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