Question

The equations below represent the numbers y of tickets sold after x weeks for two different local music festivals.

y=10x + 150
Country Music Festival
y = 20x + 115
Pop Music Festival
After how much time have the same number of tickets been sold for both festivals?
weeks
What is the number of tickets sold at that time?
tickets
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Answer 1

Part a) 3.5 weeks

Part b) 185 tickets

Explanation:

Part a) After how much time have the same number of tickets been sold for both festivals?

Let

x -----> the number of weeks

y ----> the number of tickets sold

we have

Country Music Festival

`y=10x+150` ----> equation A

Pop Music Festival

`y=20x+115` ----> equation B

Equate equation A and equation B

`20x+115=10x+150`

solve for x

`20x-10x=150-115`

`10x=35`

`x=3.5\ weeks`

Part b) What is the number of tickets sold at that time?

substitute the value of x=3.5 weeks in the linear equation A or linear equation B

`y=10(3.5)+150`

`y=35+150`

`y=185\ tickets`