The local amusement park is a popular field trip destination. this year the senior class at high school a and the senior class at high school b both planned trips there. the senior class at high school a rented and filled 9 vans and 5 buses with 267 students. high school b rented and filled 10 vans and 10 buses with 390 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?

The van can carry 18 students and bus can carry 21 students.

Solution:

Given that,

Senior class at high school "a" rented and filled 9 vans and 5 buses with 267 students.  

High school "b" rented and filled 10 vans and 10 buses with 390 students.  

Each van and each bus carried the same number of students.  

Let the capacity of van be "m", and capacity of bus be "n"

Then, according to given information,

For school a ⇒ 9m + 5n = 267 ⇒ (1)

For school b ⇒ 10m + 10n = 390

⇒ m + n = 39

⇒ m = 39 – n ⇒ (2)

Substitute (2) in (1)

9(39 – n) + 5n = 267  

⇒ 351 – 9n + 5n = 267  

⇒ 9n – 5n = 351 – 267  

⇒ 4n = 84  

⇒ n = 21

Then, m + 21 = 39

⇒ m = 39 – 21

⇒ m = 18

Hence, van can carry 18 students and bus can carry 21 students.

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.