Question

A school district transported a total of 409 students and teachers to a zoo in buses and vans.
-Each bus transported a total of 55 students and teachers.
-Each van transported a total of 12 students and teachers.
-There were 5 buses than vans
What is the total number of students and teachers who rode to the zoo in buses? What is the total number of students as teachers who rode to the zoo in vans?
( 18 points guaranteed)

Answer 1

Answer: There are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.

Step-by-step explanation:

Since we have given that

Total number of students and teachers = 409

Let the number of vans be x

Let the number of buses be x+5

Number of students and teachers each bus transported = 55

Number of students and teachers each van transported = 12

According to question,

$55(x+5)+12x=409\\\\55x+275+12x=409\\\\67x=409-275\\\\67x=134\\\\x=\frac{134}{67}\\\\x=2$

Total number of students and teachers who rode to the zoo in buses will be

$55(x+5)\\\\=55(2+5)\\\\=55\times 7\\\\=385$

Total number of students and teachers who rode to the zoo in vans will be

$12x\\\\=12\times 2=24$

Hence, there are 385 students and teachers who rode to the zoo in buses and 24 students and teachers who rode to the zoo in trains.