Answer:
see explanation
Explanation:
(11)
let a represent adult tickets and y represent youth tickets , then
a + y = 240 → (1) ← based on number who went on Friday night
8a + 5y = 1440 → (2) ← based on sale of tickets
multiplying (1) by - 5 and adding result to (2) will eliminate y
- 5a - 5y = - 1200 → (3)
add (2) and (3) term by term to eliminate y
(8a - 5a) + (5y - 5y) = 1440 - 1200
3a + 0 = 240
3a = 240 ( divide both sides by 3 )
a = 80
substitute a = 80 into (1) and solve for y
80 + y = 240 ( subtract 80 from both sides )
y = 160
That is 80 adult and 160 youth tickets were sold
(12)
let x and y represent the 2 types of question (x for 2 points, y for 4 points )
x + y = 40 → (1) ← number of questions asked
2x + 4y = 100 → (2) ← bases on number of points awarded
multiplying (1) by - 4 and adding the result to (2) will eliminate y
- 4x - 4y = - 160 → (3)
add (2) and (3) term by term to eliminate y
(2x - 4x) + (4y - 4y) = 100 - 160
- 2x + 0 = - 60
- 2x = - 60 ( divide both sides by - 2 )
x = 30
substitute x = 30 into (1) and solve for y
30 + y = 40 ( subtract 30 from both sides )
y = 10
That is there were 30, 2 point questions and 10, 4 point questions in the test.