Step-by-step explanation:
Let’s denote the smaller number as ( x ) and the larger number as ( y ). According to the problem, we have two equations:
The sum of the two numbers is 49: [ x + y = 49 ]
The greater number exceeds thrice the smaller number by 1: [ y = 3x + 1 ]
Now, we can solve these equations simultaneously. Substituting the second equation into the first, we get: [ x + (3x + 1) = 49 ] [ 4x + 1 = 49 ] [ 4x = 48 ] [ x = 12 ]
Now that we have the value of ( x ), we can find ( y ): [ y = 3(12) + 1 ] [ y = 36 + 1 ] [ y = 37 ]
Therefore, the larger number is 37.