Answer:
Explanation:
a) let x represent the number of $8 tickets sold.
let y represent the number of $12 tickets sold.
The total number of people that paid for tickets is 30500, it means that
x + y = 30500
The total sales from the tickets was $308000. This means that
8x + 12y = 308000- - - - - - - - - - - -1
Substituting x = 30500 - y into equation 1, it becomes
8(30500 - y) + 12y = 308000
244000 - 8y + 12y = 308000
- 8y + 12y = 308000 - 244000
4y = 64000
y = 64000/4
y = 16000
x = 30500 - y = 30500 - 16000
x = 14500
14500 eight dollar tickets and 16000 twelve dollar tickets were sold.
b) let x represent the cost of a shirt.
let y represent the cost of a pair of slacks.
5 shirts and 3 pairs of slacks cost $172. This means that
5x + 3y = 172- - - - - - - - - - -1
3 shirts and 4 pairs of slacks cost $156. This means that
3x + 4y = 156- - - - - - - - - - - -2
Multiplying equation 1 by 3 and equation 2 by 5, it becomes
15x + 9y = 516
15x + 20y = 780
Subtracting, it becomes
- 11y = - 264
y = - 264/ - 11
y = 24
Substituting y = 24 into equation 1, it becomes
5x + 3 × 24 = 172
5x + 72 = 172
5x = 172 - 72
5x = 100
x = 100/5
x = 20
Each shirt costs $20 and each pair of slacks cost $24.