Answer:
81000 people went to Bonnaroo.
192000 people went to Lollapalooza.
Step-by-step explanation:
Given:
Total number of people attending festivals, [tex]N=273000[/tex]
Number of people attending Lollapalooza is 30,000 more than twice the people attending Bonnaroo.
Unknown:
Number of people attending Lollapalooza and Bonnaroo.
Let the number of people attending Bonnaroo be [tex]x[/tex].
Therefore, the number of people attending Lollapalooza is equal to [tex]30000+2x[/tex]
Evaluate:
Sum of people attending Bonnaroo and Lollapalooza is equal to the total number of people attending the festivals. So,
[tex]x+30000+2x=N\\3x+30000=273000\\3x=273000-30000\\3x=243000\\x=\frac{243000}{3}=81000[/tex]
Substitute and Solve:
Now, we have, [tex]x=81000[/tex].
Substitute 81000 for [tex]x[/tex] and solve for the number of people attending both the festivals. This gives,
Number of people attending Bonnaroo = [tex]x=81000[/tex]
Number of people attending Lollapalooza = [tex]30000+2x=30000+2(81000)=30000+162000=192000[/tex]
Therefore, 81000 people went to Bonnaroo and 192000 people went to Lollapalooza.
