Final answer:
To find Ed and Cheryl's current ages, we start with the given ratio of their ages, 3:2, and the future ratio in 8 years, 13:10. We create a system of equations and solve for the variable representing their ages, then calculate the current ages using the initial ratio.
Step-by-step explanation:
The question is asking us to determine the current ages of Ed and Cheryl, knowing that their current ages are in a 3:2 ratio and that in 8 years the ratio of their ages will be 13:10. To solve this problem, we can set up a system of equations based on the information given.
Step-by-Step Solution:
1. Let Ed's current age be 3x and Cheryl's current age be 2x, since their ages are in a 3:2 ratio.
2. In 8 years, Ed's age will be 3x + 8 and Cheryl's age will be 2x + 8.
3. The question says that in 8 years, their ages will be in a 13:10 ratio. So we can write the equation (3x + 8) / (2x + 8) = 13/10.
4. By cross-multiplying and simplifying the equation, we get 10(3x + 8) = 13(2x + 8).
5. Solving for x gives us the value of x which can then be used to find Ed and Cheryl's current ages.
6. Substitute the value of x back into the expressions for Ed and Cheryl’s current ages (3x and 2x respectively) to get the actual ages.
Using these steps, we find the current ages of Ed and Cheryl according to the given ratios and the projected change in their ages over time.