word problem Algebra 1

Question

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 11 vans and 12 buses with 412 students. High School B rented and

filled 9 vans and 2 buses with 126 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

Hi,

The number of student in van = V

The number of student in bus = B

School A rented and filled 11 vans and 12 buses with 412 students it means:

11v + 12B = 412

filled 9 vans and 2 buses with 126 students it means: 9V + 2B = 126

now, make a system and solve it

11v + 12B = 412

9V + 2B = 126

---------------------

V = 8 & B = 27

I hope it is useful,

Minoo

Answer 2

To solve this you need to use simultaneous equations (or that's the name that I was taught). We write one for each situation. I'm using v as the variable for van and "b" for bus.

11v + 12b = 412

9v + 2b = 126 (I'll solve this one for b)

2b = 126 - 9v

b = (126 - 9v)/2

Now I'll substitute that value for b into the other equation. This leaves me with only the v variable. (algebra commentary for each step)

11v + 12((126 - 9v)/2) = 412 (substitute)

11v + (1512-108v)/2 = 412 (multiply the 12 through)

11v +756 - 54v = 412 (divide by 2)

-43v + 756 = 412 (combine "v" terms)

-43v = -344 (subtract 756 from both sides)

v = 8 (divide both sides by -43)

Now we know how many people a van holds. We can put that value in place of "v" in either expression in order to solve for b.

9(8) +2b = 126 (put 8 in for v)

72 + 2b = 126 (multiply)

2b = 54 (subtract 72 from both sides)

b = 27 (divide both sides by 2)

It's a strange bus that holds 27 students, but hey, it's a math problem. We can check that these values work by plugging them both into the other equation.

11(8) + 12(27) = 412 It works