SOLUTION: In a hall, 60% of the 2400 students are boys. Some boys went to the field to pitch tents while the rest stayed in hall and prepared food. Of the students remaining in the hall, 40%

Question 1034923: In a hall, 60% of the 2400 students are boys. Some boys went to the field to pitch tents while the rest stayed in hall and prepared food. Of the students remaining in the hall, 40% were boys. How many boys went to pitch tents?

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
2400 students.
60% are boys.
that means that .6 * 2400 = 1440 are boys.
that means that 2400 - 1440 = 960 are girls.
some of the boys went to the field to pitch tents.
this means that none of the girls went to the field to pitch tents.
40% of the students that did not go to pitch tents were boys.
you have 960 girls remaining in the hall and some boys.
the boys made up 40% of the students remaining in the hall.
let x = the number of boys who stayed behind.
they represent 40% of the total students that stayed behind.
the total students that stayed behind are x + 960.
x = 40% of that.
the equation is x = .4 * (x + 960)
simplify this equation to get x = .4x + .4*960.
simplify further to get x = .4x + 384
subtract .4x from both sides of the equation to get .6x = 384
divide both sides of this equation by .6 to get x = 384/.6 = 640.
there were 640 boys who remained in the hall and didn't go to pitch tents.
total who stayed behind were 960 + 640 = 1600.
boys were 40% of that = .4 * 1600 = 640.
since there were a total of 1440 boys and 640 stayed behind, then the number of boys who went to pitch tents is equal to 1440 - 640 = 800.
your solution is that 800 boys went to pitch tents.

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