- Kim is 12 years older than Sue.
- The sum of their ages is 27.
Let’s denote Sue’s age as SS and Kim’s age as KK.
Step-by-Step Solution:
- Set Up the Equations:
- Since Kim is 12 years older than Sue, we have:
K=S+12K = S + 12
- The sum of their ages is 27:
S+K=27S + K = 27
- Since Kim is 12 years older than Sue, we have:
- Substitute the First Equation into the Second:
Substitute K=S+12K = S + 12 into the equation S+K=27S + K = 27:
S+(S+12)=27S + (S + 12) = 27
- Solve for Sue’s Age SS:
- Combine like terms:
2S+12=272S + 12 = 27
- Subtract 12 from both sides:
2S=152S = 15
- Divide by 2:
S=7.5S = 7.5
- Combine like terms:
Conclusion:
Sue is 7.5 years old.
Thus, Kim, being 12 years older than Sue, is:
K=S+12=7.5+12=19.5K = S + 12 = 7.5 + 12 = 19.5
Therefore, Sue is 7.5 years old.
