Atheater 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? \

The no. of upper level seats tickets sold are 200

The no. of lower level seats tickets sold are 150

Step-by-step 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

⇒

⇒

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

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