A movie theater charges $10 for adults and $6 for seniors. On a particular day when 357 people paid in admission, the total receives were $2414 How many who paid were adults?

How many who paid were seniors?

Step-by-step explanation:

Determine the types of tickets involved.

There are student tickets and adult tickets.

Create a table to organize the information.

Type  

Number

Value ($)

Total Value ($)

Student    

6

Adult    

9

1

,

506

Step 2. Identify what you are looking for.

We are looking for the number of student and adult tickets.

Step 3. Name. Represent the number of each type of ticket using variables.

We know the number of adult tickets sold was  

5

 less than three times the number of student tickets sold.

Let  

s

 be the number of student tickets.

Then  

3

s

−

5

 is the number of adult tickets.

Multiply the number times the value to get the total value of each type of ticket.

Type  

Number

Value ($)

Total Value ($)

Student  

s

6

6

s

Adult  

3

s

−

5

9

9

(

3

s

−

5

)

1

,

506

Step 4. Translate: Write the equation by adding the total values of each type of ticket.

6

s

+

9

(

3

s

−

5

)

=

1506

Step 5. Solve the equation.

6

s

+

27

s

−

45

=

1506

33

s

−

45

=

1506

33

s

=

1551

s

=

47

students

Substitute to find the number of adults.

3

s

−

5

=

 number of adults

3

(

47

)

−

5

=

136

 adults

Step 6. Check. There were  

47

 student tickets at  

$6

 each and  

136

 adult tickets at  

$9

 each. Is the total value  

$1506

?

 We find the total value of each type of ticket by multiplying the number of tickets times its value; we then add to get the total value of all the tickets sold.

47

⋅

6

=

282

136

⋅

9

=

1224

1506

✓

Step 7. Answer the question. They sold  

47

 student tickets and  

136

 adult tickets.

All is the infinite pronoun