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Question

# 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?

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Solution

## 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.

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