Question

A school district transported a total of 409 students and teachers to a zoo in buses and vans.

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.