Number of Mangoes with A and B
Video Explanation
Question
A and B each have a certain number of mangoes. A says to B, “If you give me 30 mangoes, I will have twice as many as left with you.” B replies, “If you give me 10 mangoes, I will have thrice as many as left with you.” Find how many mangoes each has.
Solution
Step 1: Let the Variables
Let the number of mangoes with A = \(x\)
Let the number of mangoes with B = \(y\)
Step 2: Form the Equations
If B gives 30 mangoes to A:
A will have \(x + 30\) B will have \(y – 30\)
According to the condition:
\[ x + 30 = 2(y – 30) \]
\[ x + 30 = 2y – 60 \]
\[ x – 2y = -90 \quad (1) \]
If A gives 10 mangoes to B:
A will have \(x – 10\) B will have \(y + 10\)
According to the condition:
\[ y + 10 = 3(x – 10) \]
\[ y + 10 = 3x – 30 \]
\[ -3x + y = -40 \quad (2) \]
Step 3: Solve by Elimination Method
Multiply equation (1) by 3:\[ 3x – 6y = -270 \quad (3) \]
Add equation (2) and (3):\[ (3x – 6y) + (-3x + y) = -270 – 40 \]
\[ -5y = -310 \]
\[ y = 62 \]
Step 4: Find the Value of x
Substitute \(y = 62\) in equation (1):\[ x – 2(62) = -90 \]
\[ x – 124 = -90 \]
\[ x = 34 \]
Conclusion
Number of mangoes with A:
\[ \boxed{34} \]
Number of mangoes with B:
\[ \boxed{62} \]
Final Answer (For Exam)
A has 34 mangoes
B has 62 mangoes