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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?
What is the number of tickets sold at that time?

Respuesta :

sarah6572
assuming you mean y=10x+150 and y=20x+115, you need to use a simultaneous equation, because you have two equations with two unknowns (x and y)

rearrange so
10x-y=-150
20x-y=-115

multiply the top by -1, so that if we add the two lines together, the y will cancel out
-10x+y=150
20x-y=-115

add the two lines together
10x=35
x=3.5

so the time is 3 and a half weeks

then we can sub in x to find y
20x-y=-115
20(3.5)-y=-115
70-y=-115
-y=-185
y=185

so 185 tickets were sold !
you can sub these values into your original equations to check your answer :)

After three and half weeks , same number of tickets been sold for both festivals.

The number of tickets sold at that time is 185.

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

 Country Music Festival, [tex]y=10x+150[/tex]

 Pop Music Festival,    [tex]y=20x+115[/tex]

To find time for which the same number of tickets been sold for both festivals.

Equate both equation shown above.

      [tex]10x+150=20x+115\\\\20x-10x=150-115\\\\10x=35\\\\x=35/10=3.5 weeks[/tex]

the number of tickets sold at that time is,

        [tex]y=10x+150=10(3.5)+150=185[/tex] tickets.

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