Greg is 16 years older than his sister Barbra. In 13 years , he will be twice as old as Barbra. How old is each of them now ?
Sol: x+16+13 = 2x+26
x+29 = 2x+26
29-26 = 2x-x
3 = x barbara
3+16 = 19 greg
To solve this problem, we can use algebra to set up a system of equations based on the given information. Let's represent Greg's current age as 'G' and Barbra's current age as 'B'.
According to the problem, "Greg is 16 years older than his sister Barbra," so we can write the equation:
G = B + 16
In 13 years, "he will be twice as old as Barbra." This can be written as:
G + 13 = 2(B + 13)
Now, we have a system of two equations:
1. G = B + 16
2. G + 13 = 2(B + 13)
To solve this system, we can substitute equation 1 into equation 2:
(B + 16) + 13 = 2(B + 13)
B + 29 = 2B + 26
B - 2B = 26 - 29
-B = -3
Dividing both sides of the equation by -1, we get:
B = 3
Now, substitute the value of B back into equation 1:
G = B + 16
G = 3 + 16
G = 19
Therefore, Greg is 19 years old and Barbra is 3 years old.
g = b+16
g+13 = 2(b+13)
now just solve for g and b.