Explanation:
To solve this problem, let's assume that the amount of money Joseph and Alvira initially had is represented by the variable "x". After Joseph lent $13 to Alvira, Joseph would have x - 13 dollars, while Alvira would have x + 13 dollars.
According to the given information, Alvira had 3 times as much money as Joseph after receiving the $13 loan. Mathematically, we can express this as:
x + 13 = 3(x - 13)
Let's solve this equation to find the value of x:
x + 13 = 3x - 39
2x = 52
x = 26
Therefore, Joseph and Alvira initially had $26 each.
To find out how much Alvira had in the end, we need to substitute the value of x back into the equation:
Alvira's final amount = x + 13
= 26 + 13
= 39 dollars.
So, Alvira had $39 in the end.