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Priyanka and arti decided to doneate Rs ...

Priyanka and arti decided to doneate Rs 1600 for the army windows let priyanka 's shares as 'x' and arti share as'y'
(a) form a lienar equation in two variables
(b) if priyanka donates thrice the amount donated by arti then find out the amount donated by both

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To solve the problem step by step, we will follow the instructions given in the question. ### Step 1: Form a Linear Equation Let Priyanka's share be represented by \( x \) and Aarti's share be represented by \( y \). According to the problem, the total amount donated by both is Rs. 1600. Therefore, we can write the equation as: \[ x + y = 1600 \] ### Step 2: Formulate the Second Equation The problem states that Priyanka donates thrice the amount donated by Aarti. This can be expressed as: \[ x = 3y \] ### Step 3: Substitute the Second Equation into the First Equation Now we will substitute the value of \( x \) from the second equation into the first equation: \[ 3y + y = 1600 \] ### Step 4: Combine Like Terms Combine the terms on the left side of the equation: \[ 4y = 1600 \] ### Step 5: Solve for \( y \) Now, divide both sides of the equation by 4 to find the value of \( y \): \[ y = \frac{1600}{4} = 400 \] ### Step 6: Find the Value of \( x \) Now that we have \( y \), we can find \( x \) using the equation \( x = 3y \): \[ x = 3 \times 400 = 1200 \] ### Conclusion Thus, Priyanka donated Rs. 1200 and Aarti donated Rs. 400. ### Summary of the Solution - Priyanka's donation (x) = Rs. 1200 - Aarti's donation (y) = Rs. 400 ---
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