Question

India is the largest producer of Apple fruit. Apple is a rich antioxidant fruit. Antioxidants are disease-fighting compounds; they prevent and repair oxidation damage that happens during normal cell activity. Due to rich nutritive value, a school distributes 300 apples equally among a certain number of students. Had there been 10 more students, each would have received one apple less. Find the number of students.

Answer 1

Hint: Inequality is the relation which compares the unequal numbers. It basically used to equate the unequal numbers when there are changes made. In a given relation whenever changes are made one of its terms is kept constant, hence we take that term as the base, and then the equation is solved.

Complete step by step solution:
Let the number of students be \[x\] among whom the apples are to be distributed, hence the number of apples each student will get \[y = \dfrac{{300}}{x}\]-- (i), where y is the number of apples each student would get.
Now given the number of students is increased the new total no. of students will be \[ = x + 10\] hence each student would get \[1\] apple less\[ = y - 1\]. So we can write
\[\left( {y - 1} \right) = \dfrac{{300}}{{x + 10}}\]--- (ii)
Now solve both the equations to find the value of \[x\]in equation-- (i)
\[ y = \dfrac{{300}}{x} \\
  300 = xy \\ \]
Now put \[300 = xy\] in equation--(ii)
\[ \left( {y - 1} \right) = \dfrac{{300}}{{x + 10}} \\
  \left( {y - 1} \right)\left( {x + 10} \right) = xy \\
  xy + 10y - x - 10 = xy \\
  10y - x = 10 \\
  y = \left( {\dfrac{{x + 10}}{{10}}} \right) \\ \]
Hence we get \[y = \left( {\dfrac{{x + 10}}{{10}}} \right)\], now put this in equation-- (i) to find the value of \[x\]\[
  y = \dfrac{{300}}{x} \\
  \left( {\dfrac{{x + 10}}{{10}}} \right) = \dfrac{{300}}{x} \\
    \\ \]
\[x\left( {x + 10} \right) = 3000\] [By cross multiplying]
\[ {x^2} + 10x = 3000 \\
  {x^2} + 10x - 3000 = 0 \\
  {x^2} + 60x - 50x - 3000 = 0 \\
  x\left( {x + 60} \right) - 50\left( {x + 60} \right) = 0 \\
  \left( {x - 50} \right)\left( {x + 60} \right) = 0 \\ \]
By solving the quadratic equation we get the value of \[x = 50, - 60\] since the number of students cannot be negative, hence we take the number of students to be \[x = 50\].

Note: Whenever we are asked to find the value or quantity of something then their value can never be considered as negative. Students are advised to read these types of questions carefully as the language of the question is a bit confusing.