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Step-by-step 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.

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