Question

6

James bought 16 tickets for a concert. The good tickets cost $8 and bad tickets
cost $5. He spent a total of $113 on all the tickets. Write a system that can be used to
determine how many good tickets James bought and how many bad ticket he bought.

Answer 1

James bought 11 good tickets and 5 bad tickets.

Explanation:

Given that:

Cost of each good ticket = $8

Cost of each bad ticket = $5

Total amount spent = $113

Total tickets bought = 16

Let,

x be the number of good tickets bought

y be the number of bad tickets bought

x+y=16 Eqn 1

8x+5y=113 Eqn 2

Multiplying Eqn 1 by 5

5(x+y=16)

5x+5y=80 Eqn 3

Subtracting Eqn 3 from Eqn 2

(8x+5y)-(5x+5y)=113-80

8x+5y-5x-5y=33

3x=33

Dividing both sides by 3

`(3x)/(3)=(33)/(3)\\x=11`

Putting x=11 in Eqn 1

11+y=16

y=16-11

y=5

Hence,

James bought 11 good tickets and 5 bad tickets.