There are benches in class room .If 4 students sit on each bench ,3 benches are left vacant and if 3 students sit on each bench , 3 students are left standing .what is the total number of students in the class?
This is more explained solution for your understanding. You can remove whatever is unnecessary. All the best.
SOLUTION
let x equal the number of benches.
let y equal the number of students.
when there are 4 students to a bench, then there are 3 benches left over.
this means that y = 4x - 12.
that formula states that the number of students is equal to 4 times the number of benches - 12 students.
the 12 students that are subtracted are the 4 students per bench for the 3 benches that are empty.
when there are 3 students to a bench, then there are 3 students left over.
this means that y = 3x + 3.
that formula states that the number of students is equal to 3 times the number of benches plus 3 students.
the 3 students that are added are the 3 students that could not fit on any of the benches because there were only 3 students per bench.
you have 2 equations that need to be solved simultaneously.
they are:
y = 4x - 12
y = 3x + 3
in the second equation, substitute 4x - 12 for y and you get:
4x - 12 = 3x + 3
solve for x to get x = 15.
the number of benches has to be 15 if the calculations were done correctly.
with 4 students per bench, you get 4 * 15 = 60 students.
since 3 of the benches were empty, you have to subtract 3 * 4 = 12.
you get 60 - 12 = 48 students.
with 3 students per bench, you get 3 * 15 = 45 students.
since 3 of the students couldn't fit on any of the benches, you have to add 3 students to the total.
you get 45 + 3 = 48 students.
This is more explained solution for your understanding. You can remove whatever is unnecessary. All the best.
SOLUTION
let x equal the number of benches.
let y equal the number of students.
when there are 4 students to a bench, then there are 3 benches left over.
this means that y = 4x - 12.
that formula states that the number of students is equal to 4 times the number of benches - 12 students.
the 12 students that are subtracted are the 4 students per bench for the 3 benches that are empty.
when there are 3 students to a bench, then there are 3 students left over.
this means that y = 3x + 3.
that formula states that the number of students is equal to 3 times the number of benches plus 3 students.
the 3 students that are added are the 3 students that could not fit on any of the benches because there were only 3 students per bench.
you have 2 equations that need to be solved simultaneously.
they are:
y = 4x - 12
y = 3x + 3
in the second equation, substitute 4x - 12 for y and you get:
4x - 12 = 3x + 3
solve for x to get x = 15.
the number of benches has to be 15 if the calculations were done correctly.
with 4 students per bench, you get 4 * 15 = 60 students.
since 3 of the benches were empty, you have to subtract 3 * 4 = 12.
you get 60 - 12 = 48 students.
with 3 students per bench, you get 3 * 15 = 45 students.
since 3 of the students couldn't fit on any of the benches, you have to add 3 students to the total.
you get 45 + 3 = 48 students.
