Answer:
larger number x = 37 and smaller number y = 12
Step-by-step explanation:
Let the larger number be x and the smaller number be y.
Sum of the numbers is [tex]x + y = 49[/tex] ....(1)
∴ [tex]y = 49 - x[/tex]
Now, 3 times of the smaller number = 3y
According to question,
[tex]x = 3y + 1 ......(2)[/tex]
Now, by substituting the value of y in (2)
[tex]x = 3 (49 - x) + 1[/tex]
[tex]x = 147 - 3x + 1[/tex]
[tex]x + 3x = 148[/tex]
[tex]4x = 148[/tex]
[tex]x = 37[/tex]
Now,y = 49 - x and [tex]x = 37[/tex]
[tex]y = 49 - 37 = 12[/tex]
So the larger number x =37 and smaller number y = 12.
Since larger of two numbers is one more than three times the smaller number, the numbers are 37 and 12 respectively.
Translating the word problem into an algebraic expression, we have;
For larger number:
[tex]L = 3S + 1[/tex]
For sum of the two numbers:
[tex]L + S = 49[/tex]
Substituting eqn 1 into eqn 2, we have:
[tex]3S + 1 + S = 49\\\\4S + 1 = 49\\\\4S = 49 -1\\\\4S = 48\\\\S = \frac{48}{4}[/tex]
S = 12
For larger number:
[tex]L = 3S + 1\\\\L = 3(12) + 1\\\\L = 36 +1[/tex]
L = 37
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