Question

A theater sells tickets for a concert. Tickets for lower-level seats sell for $35 each, and tickets for upper-level seats sell for $25 each. The theater sells 350 tickets for $10,250. How many tickets of each type were sold?\

Answer 1

a*25+b*35=10250
a +b = 350 | * -25

25a + 35b= 10. 250
-25a -25 b= -8.750
------------------------------
10b = 1500
b=1500:10
b=150 tickets cost 35 $
a= 350-150
a= 200 tickets cost 25 $

Answer 2

The no. of upper level seats tickets sold are 200

The no. of lower level seats tickets sold are 150

Explanation:

Given : theater sells tickets for a concert. Tickets for lower-level seats sell for $35 each, and tickets for upper-level seats sell for $25 each. The theater sells 350 tickets for $10,250.

To Find: How many tickets of each type were sold?

Solution :

Let x be the no. of lower level seats tickets sold

Let y be the no. of upper level seats tickets sold

Cost of 1 lower level seats ticket sold = $35

Cost of x lower level seats ticket sold = $35x

Cost of 1 upper level seats ticket sold = $25

Cost of y upper level seats ticket sold = $25y

Since the theatre sold tickets for $10250

⇒35x+25y=10250 --a

Since we are also given that they sold 350 tickets

x+y=350 ---(b)

Solving a and b using substitution method

Substitute the value of x from b in a

⇒35(350-y)+25y=10250

⇒12250-35y+25y=10250

⇒12250-10y=10250

⇒12250-10250=10y

⇒2000=10y

⇒
`(2000)/(10)=y`

⇒
`200=y`

Thus the no. of upper level seats tickets sold are 200

Putting this value of y in eqn b to get value of x

x+200=350

x=350-200

x=150

Thus the no. of lower level seats tickets sold are 150