SOLUTION: 19. This year the senior class at West High School and the senior class at South High School both planned trips to the state fair. The senior class at West High rented and filled

Algebra ->  Linear-equations -> SOLUTION: 19. This year the senior class at West High School and the senior class at South High School both planned trips to the state fair. The senior class at West High rented and filled       Log On


   

Question 206102: 19. This year the senior class at West High School and the senior class at South High School both planned trips to the state fair. The senior class at West High rented and filled 6 vans and 9 buses with 459 students. South High rented and filled 3 vans and 7 buses with 337 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?

Answer by Targetweek(62) About Me  (Show Source):
You can put this solution on YOUR website!
1. First set up 2 equations
- 6v%2B9b+=+459
- 3v%2B7b+=+337
2. Then change one of the equations so that when combined one of the variables will cancel out
- 6v%2B9b+=+459
- -2%283v%2B7b%29+=+%28337%29%28-2%29
- -6v-14b+=+-674
so...
- 6v%2B9b+=+459
- -6v-14b+=+-674
+______________________
= 0-5b+=+-215
a. Then solve for b
- -5b+=+-215
- %28-1%2F5%29%28%28-5b%29%2F1%29+=+%28-215%29%2F%28-5%29
= b+=+43
3. So each bus holds 43 kids
4. Now plug in b=43 into the first equation and solve for v
- 6v%2B9%2843%29+=+459
- 6v+%2B+387+=+459
- 6v+%2B387-387+=+459-387
- 6v+=+72
- 6v%2F6+=+72%2F6
= v+=+12
5. So each van holds 12 kids
6. your answer is b = 43 and v = 12