This year Ben is 4/7 as old as Glen. Fifteen years from now, Ben will be ¾ as old as Glen. At that time, the sum of their ages will be 63. How old are Ben and Glen now?
G = Glen's present age
B = Ben's present age
B = 4/7 G
G + 15 + B + 15 = 63
substitute, B = 4/7 G
G + 15 + 4/7 G + 15 = 63
Solve for G
To solve this problem, we can set up a system of equations based on the given information.
Let's assume Ben's current age is x and Glen's current age is y.
According to the problem, "This year Ben is 4/7 as old as Glen." This can be written as: x = (4/7)y.
Also, it states "Fifteen years from now, Ben will be ¾ as old as Glen, and the sum of their ages will be 63." This can be written as: (x + 15) = (3/4)(y + 15) and (x + 15) + (y + 15) = 63.
Now, we have two equations:
1) x = (4/7)y
2) (x + 15) = (3/4)(y + 15) and (x + 15) + (y + 15) = 63.
To solve these equations, we can substitute the value of x from equation 1 into equation 2.
1) x = (4/7)y
2) ((4/7)y + 15) = (3/4)(y + 15) and ((4/7)y + 15) + (y + 15) = 63.
Next, we can simplify equation 2:
((4/7)y + 15) = (3/4)(y + 15)
Multiplying both sides by 4:
4((4/7)y + 15) = 3(y + 15)
16/7y + 60 = 3y + 45
16/7y - 3y = 45 - 60
16/7y - 21/7y = -15/1
-5/7y = -15
Multiplying both sides by -7/5:
(-5/7y)(-7/5) = (-15)(-7/5)
y = 21
Now that we have y = 21, we can substitute this value back into equation 1 to find x:
x = (4/7)y
x = (4/7) * 21
x = 12
Therefore, Ben is currently 12 years old and Glen is currently 21 years old.