Sarika distributes chocolates on the occasion of children 's day she gives 5 chocolates to each child and 20 chocolates to adults if number of children is represented by 'x' and total distrubuted chocolates as 'y'
(i) write it in the form of linear equation in two variables
(ii) if she distributed 145 chocolates in total find number of children

Answer

To solve the problem step by step, we will follow the two parts of the question.

### Part (i): Writing the Linear Equation

1. **Understanding the problem**: Sarika gives 5 chocolates to each child and 20 chocolates to each adult. The number of children is represented by \( x \) and the total number of distributed chocolates is represented by \( y \).

2. **Formulating the equation**:
- Chocolates given to children: Each child receives 5 chocolates, so for \( x \) children, the total chocolates given to children is \( 5x \).
- Chocolates given to adults: Each adult receives 20 chocolates. If we denote the number of adults as \( a \), then the total chocolates given to adults is \( 20a \).
- Therefore, the total chocolates distributed can be expressed as:
\[ y = 5x + 20a \]
- This is the linear equation in two variables \( x \) and \( y \).

### Part (ii): Finding the Number of Children when Total Chocolates are 145

1. **Setting up the equation with given values**: We know that the total number of distributed chocolates \( y \) is 145. Thus, we can substitute \( y \) in the equation:
\[ 145 = 5x + 20a \]

2. **Rearranging the equation**: To find \( x \), we need to express \( a \) in terms of \( x \) or vice versa. However, we can assume that there are no adults (i.e., \( a = 0 \)) for simplicity in finding the number of children:
\[ 145 = 5x + 20(0) \implies 145 = 5x \]

3. **Solving for \( x \)**:
- Rearranging gives:
\[ 5x = 145 \]
- Dividing both sides by 5:
\[ x = \frac{145}{5} = 29 \]

4. **Conclusion**: The number of children \( x \) is 29.

### Summary of the Solution:
- The linear equation is \( y = 5x + 20a \).
- When \( y = 145 \) and assuming \( a = 0 \), the number of children \( x \) is 29.