The sum of the ages of John and Sarah is 26. Five years ago, John was three times as old as Sarah. How old is John now?a.9b.12c.17d.22
Question
The sum of the ages of John and Sarah is 26. Five years ago, John was three times as old as Sarah. How old is John now?a.9b.12c.17d.22
Solution
Let's solve this step by step:
Step 1: Let's denote John's current age as J and Sarah's current age as S. From the problem, we know that J + S = 26.
Step 2: We also know that five years ago, John was three times as old as Sarah. So, J - 5 = 3(S - 5).
Step 3: Now we have a system of two equations, and we can solve it. Let's substitute S from the first equation (S = 26 - J) into the second one:
J - 5 = 3((26 - J) - 5)
Step 4: Simplify the equation:
J - 5 = 3(21 - J)
J - 5 = 63 - 3J
Step 5: Combine like terms:
4J = 68
Step 6: Divide by 4 to solve for J:
J = 68 / 4 = 17
So, John is 17 years old now, which corresponds to option c.
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