The sum of the ages of Spencer and Raquel is 51 years. 6 years ago, Spencer's age was 2 times Raquel's age. How old is Spencer now?
s+r = 51 so r = 51-s
s-6 = 2(r-6)
substitute
s-6 = 2 (51 - s - 6) = 2(45-s) =90-2s
3 s = 96
To find out how old Spencer is now, we can set up a system of equations based on the given information.
Let's say S represents Spencer's current age, and R represents Raquel's current age.
We are given two pieces of information:
1. The sum of their ages is 51 years: S + R = 51.
2. Six years ago, Spencer's age was 2 times Raquel's age: (S - 6) = 2(R - 6).
Now, we can solve this system of equations to find the values of S and R.
1. From the first equation, we can express S in terms of R: S = 51 - R.
2. Substitute that expression for S in the second equation: (51 - R - 6) = 2(R - 6).
Now, simplify and solve for R:
45 - R = 2R - 12.
Combine like terms:
3R = 57.
Divide both sides by 3:
R = 19.
Now, substitute the value of R back into the first equation to find S:
S + 19 = 51.
S = 32.
So, Spencer is currently 32 years old.