A family bought a total of 13 tickets to a magic show, some adult and some child. The family paid a total of $85 Adult tickets are $15 each and child tickets are $5 each.
Let x represent adult tickets and y represent child tickets.
Write an equation to model the total amount of money that they spent.

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

Step-by-step explanation:

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?

Solution:

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

quantityvaluetotal$3 tickets$2 ticketstogether

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 ticketsy22ytogether350950

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

Question 1 a: $24.5 b: $10.5 c: 3/10

Step-by-step explanation:

A: 7/10 = 0.7

0.7 * 35 = 24.5

B: $35 - $24.5 = $10.5

C: Since it is 7/10 of the normal cost, you save 3/10.

Checking the work: 3/10 = 0.3

0.3 * 35 = 10.5, or the amount you saved.