Answer:
2 and 13
Step-by-step explanation:
We can use systems of equations here to find both the numbers. Let's assume one of the numbers is [tex]x[/tex] and the other is [tex]y[/tex].
We know that these numbers add up to 15, so [tex]x + y = 15[/tex].
We also know that one of these numbers is 7 more than 3 times the other, so [tex]x = 3y + 7[/tex].
We can now substitute the equation [tex]x = 3y + 7[/tex] into [tex]x + y = 15[/tex].
[tex](3y + 7) + y = 15[/tex]
Combine like terms:
[tex]4y + 7 = 15[/tex]
Subtract 7 from both sides:
[tex]4y = 8[/tex]
Divide both sides by 4:
[tex]y = 2[/tex].
Now that we know the value of [tex]y[/tex], we can substitute it inside an equation to find [tex]x[/tex]. Let's substitute it inside [tex]x + y = 15[/tex].
[tex]x + 2 = 15\\\\x = 15-2\\\\x = 13[/tex]
So the two numbers are 2 and 13.
Hope this helped!
