Question

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

Answer 1

Answer:

Part a) 3.5 weeks

Part b) 185 tickets

Step-by-step 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

$y=10(3.5)+150$

$y=35+150$

$y=185\ tickets$