The sum of Billy's and his sister Diane ages is 37. If three years ago Billy was 11 years older than Diane, then what is the age of each of them right now?
11+d=b
b+3 +d=37
so..
plug in the top equation to the bottom and you get
d+11 +d=37
so 2d=26
divide and you get d=13 plug this into the top equation and you get
b=24
so
answer:
b=24
d=13
and you check by adding both and they equal 37
To solve this problem, we can set up a system of two equations based on the information given.
Let's assume Billy's current age is represented by "B" and Diane's current age is represented by "D".
From the problem, we know that their current ages sum up to 37, so we can write the first equation:
B + D = 37 (Equation 1)
We are also given the information that three years ago, Billy was 11 years older than Diane, which gives us the second equation:
(B - 3) = (D - 3) + 11 (Equation 2)
Now, we can solve the system of equations to find the values of B and D.
From Equation 1, we can re-arrange it to express B in terms of D:
B = 37 - D
Substituting this into Equation 2, we get:
(37 - D - 3) = (D - 3) + 11
Now, simplify the equation:
34 - D = D + 8
Combine like terms:
-D - D = 8 - 34
-2D = -26
Divide both sides by -2:
D = (-26) / (-2)
D = 13
Now that we have found the value of D, we can substitute it back into Equation 1 to find B:
B + 13 = 37
B = 37 - 13
B = 24
Therefore, Billy's age right now is 24, and Diane's age right now is 13.