SOLUTION: Hi 9 out of every 20 pupils take a bus to school. The rest either by car or van. The ratio of the pupils who go by bus to those by van is 3 to 1. How many pupils are in the schoo

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Hi 9 out of every 20 pupils take a bus to school. The rest either by car or van. The ratio of the pupils who go by bus to those by van is 3 to 1. How many pupils are in the schoo      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1118395: Hi
9 out of every 20 pupils take a bus to school. The rest either by car or van. The ratio of the pupils who go by bus to those by van is 3 to 1. How many pupils are in the school if 720 go by car.
thanks
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
b, by bus
c, by car
v, by van

The description is these three equations:
system%289%2F20=b%2F%28b%2Bc%2Bv%29%2Cb%2Fv=3%2Cc=720%29

The first 9%2F20 proportion can be expressed as 9%2F20=%283v%29%2F%283v%2B720%2Bv%29.
.
.
highlight%28v=270%29------go on from there.

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The solution (or partial solution) by the other tutor is fine; and finding the solution using formal algebra can be a good exercise in the use of algebra. But if an algebraic solution is not required, the answer can be found with much less work.

9 out of 20 students take a bus. One-third as many come by van; that is 3 out of 20.

The remaining 8 out of 20 come by car; that is 720 students.

Using mental arithmetic 8 out of 20 being 720 means 1 out of 20 is 90; the number of students in the school is then 20*90 = 1800.