Kim's age is twice that of her sister. When you add Kim's age to her sister's age. you get 36. How old is each sister?

Question

(a) Write an equation that represents the situation. Explain any variable used.
(b) Solve the equation from part (a). SHow your work. State your solution as a complete very small sentence.

Answer 1

(a) Let \( K \) represent Kim's age and \( S \) represent her sister's age. According to the problem, we have the following two equations:

1. \( K = 2S \) (Kim's age is twice that of her sister.)
2. \( K + S = 36 \) (The sum of their ages is 36.)

(b) We can substitute the first equation into the second. From equation 1, we replace \( K \) in equation 2:

\[ 2S + S = 36 \]

Now, combine the terms:

\[ 3S = 36 \]

Next, divide both sides by 3 to solve for \( S \):

\[ S = \frac{36}{3} = 12 \]

Now that we know the sister's age, we can find Kim's age using the first equation:

\[ K = 2S = 2 \times 12 = 24 \]

Thus, Kim's age is 24, and her sister's age is 12.

In conclusion, Kim is 24 years old and her sister is 12 years old.