Algebra 1 question

Question

The senior classes at High School A and High School B planned separate trips to the water park. The senior class at

High School A rented and filled 7 vans and 12 buses with 554 students. High School B rented and filled 14 vans and

4 buses with 348 students. Each van and each bus carried the same number of students. Find the number of

students in each van and in each bus.

Answer 1

Let v = the number of students in a van and b = the number in a bus.

7v + 12b = 554

14v +4b = 348

Subtract 3 times equation 2 from equation 1

7v + 12b = 554

-42v -12b = -1044

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-35v + 0 = -490

v = 490/35 = 14

Substitute 14 for v in the first equation

7(14)+12b = 554

12b = 554 - 98 = 456

b = 456/12 = 38

There were 14 students in each van and 38 students in each bus.

Answer 2

Define 2 variables:

v: capacity of each van

b: capacity of each bus

From school A we have, 7v + 12b = 554

From school B we have, 14v + 4b = 348

Solving the system by elimination seems a good choice (for work by hand, that is. If graphing is an option, graph those 2 lines on desmos and it will show you the pt of intersection: (v,b)).

Multiply the top equation by -2 then add left-hand sides together and right-hand sides together to get -20b = -760 and continue ...