Question

Group a filled 2 vans and 5 buses with 202 students. Group b filled 10 vans and 13 buses with 578 students. Each can and bus carried the same amount of students. Find the number of kids in each van and in each bus

Answer 1

Answer: the number of students in each van is 11

the number of students in each bus is 36

Step-by-step explanation:

Let x represent the number of students in each van.

Let y represent the number of students in each bus.

Group a filled 2 vans and 5 buses with 202 students. This means that

2x + 5y = 202 - - - - - - - - -1

Group b filled 10 vans and 13 buses with 578 students. This means that

10x + 13y = 578 - - - - - - - - - - 2

Multiplying equation 1 by 10 and equation 2 by 2, it becomes

20x + 50y = 2020

20x + 26y = 1156

Subtracting

24y = 864

y = 864/24 = 36

Substituting y = 36 into equation 1, it becomes

2x + 5×36 = 202

2x + 180 = 202

2x = 202 - 180 = 22

x = 22/2 = 11