Each person in a group of teachers and students is given the same number of chocolates as the number of students. If 4 more students are added then in order to have the same number of chocolates per person as earlier, 28 more chocolates are needed. The total number of students now is
This problem involves setting up algebraic equations based on the given information about teachers, students, and chocolates.
Students and Chocolates Problem Setup
Let's define our variables:
- Let $T$ be the number of teachers.
- Let $S$ be the initial number of students.
- The total number of people initially is $T + S$.
Initially, each person (teachers and students) receives the same number of chocolates as the number of students. So, each person gets $S$ chocolates.
The initial total number of chocolates distributed is the total number of people multiplied by the number of chocolates per person:
\( \text{Initial Total Chocolates} = (T + S) \times S \)
Solving the Problem with More Students
Now, 4 more students are added to the group.
- The new number of students is $S + 4$.
- The total number of people now is $T + (S + 4) = T + S + 4$.
The number of chocolates per person remains the same as earlier, which is $S$ chocolates per person.
The new total number of chocolates distributed is the new total number of people multiplied by the number of chocolates per person:
\( \text{New Total Chocolates} = (T + S + 4) \times S \)
According to the problem, 28 more chocolates are needed in the new scenario compared to the initial one. This means:
\( \text{New Total Chocolates} = \text{Initial Total Chocolates} + 28 \)
Substitute the expressions for the total chocolates:
\( (T + S + 4) \times S = (T + S) \times S + 28 \)
Expand both sides of the equation:
\( TS + S^2 + 4S = TS + S^2 + 28 \)
Now, we can simplify the equation by subtracting $TS$ and $S^2$ from both sides:
\( 4S = 28 \)
To find the value of $S$, divide both sides by 4:
\( S = \frac{28}{4} \)
\( S = 7 \)
So, the initial number of students was 7.
Total Students Now
The question asks for the total number of students now. The number of students initially was 7, and 4 more students were added.
\( \text{Total Students Now} = \text{Initial Students} + 4 \)
\( \text{Total Students Now} = 7 + 4 \)
\( \text{Total Students Now} = 11 \)
Therefore, the total number of students now is 11.
Important Questions from Numerical Ability
Let m and n be two positive integers such that m + n + mn = 118. Then the value of m + n is
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