Solving for the Largest Number
We are given the sum and difference of two numbers and need to find the larger one.
Problem Setup
Let the two numbers be $x$ and $y$, where $x$ represents the largest number.
We can set up two equations based on the given information:
- Sum: $x + y = 33$
- Difference: $x - y = 13$
Calculating the Largest Number
To find the value of $x$, we can add the two equations together. This method eliminates $y$.
Equation 1: $x + y = 33$
Equation 2: $x - y = 13$
Add Equation 1 and Equation 2:
$ (x + y) + (x - y) = 33 + 13 $
Simplifying the equation:
$ 2x = 46 $
Solve for $x$ by dividing both sides by 2:
$ x = \frac{46}{2} $
$ x = 23 $
Result
The largest number is 23.
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Important Questions from Linear Equation in 2 Variable
The sum of two numbers m and n is 84 (m > n) and their difference is 6. What is the ratio of the two numbers?
A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter was to cost Rs. 1 lesser, then the total cost would remain unchanged. How long is the piece of cloth?
A. 10 m
B. 14 m
C. 12 m
D. 8 m
What historic achievement did Manu Bhaker accomplish at the 2024 Paris Olympics?
The sum of a two digit number and the number formed by interchanging its digit is 132. If nine is subtracted from the first number, the new number is 3 more than 6 times of the sum of the digits in the first number. Find the first number.
Which of the following options is the solution of the given equation:-
2x - 4y = 16
A. (8, -1)
B. (5, -5)
C. (6, -1)
D. (9, 2)
