To solve this problem, let’s define the ages of Harvey and Jane using algebraic expressions.
Let J represent Jane’s age. Since Harvey is three times as old as Jane, we can express Harvey’s age as 3J.
According to the information provided in the question, we know that the sum of their ages is 48 years. Therefore, we can set up the following equation:
J + 3J = 48
This simplifies to:
4J = 48
Now, to find Jane’s age, we divide both sides of the equation by 4:
J = 48 / 4
Hence, J = 12. This means that Jane is 12 years old.
Next, we can find Harvey’s age by substituting Jane’s age back into the expression for Harvey:
Harvey’s Age = 3J = 3 * 12
Calculating this gives us:
Harvey’s Age = 36
In conclusion:
- Jane is 12 years old.
- Harvey is 36 years old.