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Question
In a student dormitory there was enough food to feed 300 students for 15 days, Became of admission of some new students the food only lasted for 10 days . How many new students are admitted to the dormitory?
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ANSWER : 3
Descrption
<p style="margin-left:0px;">Let's denote the initial number of students in the dormitory as "N," and the rate at which food is consumed by each student per day as "R" (measured in student-days per day). We're given that initially, there was enough food to feed 300 students for 15 days, so:</p><p style="margin-left:0px;">Initial food supply = N * R * 15</p><p style="margin-left:0px;">Now, due to the admission of some new students, the food only lasted for 10 days, so:</p><p style="margin-left:0px;">Remaining food supply = (N + X) * R * 10, where "X" represents the number of new students admitted.</p><p style="margin-left:0px;">Since the amount of food is the same in both cases, we can set the two expressions equal to each other:</p><p style="margin-left:0px;">N * R * 15 = (N + X) * R * 10</p><p style="margin-left:0px;">Now, we can cancel out the common factor of "R" on both sides of the equation:</p><p style="margin-left:0px;">N * 15 = (N + X) * 10</p><p style="margin-left:0px;">Now, we can solve for "X," the number of new students admitted:</p><p style="margin-left:0px;">15N = 10(N + X)</p><p style="margin-left:0px;">15N = 10N + 10X</p><p style="margin-left:0px;">Subtract 10N from both sides:</p><p style="margin-left:0px;">5N = 10X</p><p style="margin-left:0px;">Divide both sides by 5 to solve for "X":</p><p style="margin-left:0px;">X = (5N) / 10</p><p style="margin-left:0px;">X = (1/2) * N</p><p style="margin-left:0px;">Now, we're given that X should be an integer because we can't admit a fraction of a student. Therefore, (1/2) * N must be a whole number.</p><p style="margin-left:0px;">To find out how many new students were admitted, we need to find a value of "N" where (1/2) * N is a whole number. Since we're looking for the number of new students, we want to find a value of "N" such that (1/2) * N is an integer.</p><p style="margin-left:0px;">If we let "N" be a multiple of 2, then (1/2) * N will be a whole number. Let's try "N = 300" because it's given that initially, there was enough food for 300 students:</p><p style="margin-left:0px;">X = (1/2) * 300 X = 150</p><p style="margin-left:0px;">So, if "N" was initially 300 students, then 150 new students were admitted to the dormitory.</p>
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