SOLUTION: A fine arts center charges $20 per adult and $10 per senior citizen for its performances.
On a recent event when 511 people paid admission the total receipts were $7020.
Question 1110523: A fine arts center charges $20 per adult and $10 per senior citizen for its performances.
On a recent event when 511 people paid admission the total receipts were $7020.
How many senior citizens attended the event??
You must use a system of linear equations to solve; show all logic and work.
a + s = 511, (1) (counting adults "a" and senior citizens "s")
20a + 10s = 7020. (2) (counting dollars).
Equations (1) and (2) form the system of two equations in two unknowns, "a" and "s".
Use the Elimination method to solve the system.
For it, multiply eq(1) by 10 (both sides). You will get
10a + 10s = 5110, (1')
20a + 10s = 7020. (2')
------------------------------------ Now subtract eq(1') from eq(2') (both sides).
The terms "10s" will cancel each other,
And you will get a single equation for single unknown "a".
It is how the Elimination method works.
20a - 10a = 7020 - 5110 = 1910
10a = 1910 ====> a = = 191.
Answer. 191 adults and the rest 511 - 191 = 320 senior citizens.
Solved. // On the way, you learned on how the Elimination method works.
