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.

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents