Answer:
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
⇒[tex]\frac{2000}{10}=y[/tex]
⇒[tex]200=y[/tex]
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
