Jack is married to Jill. Their son, Junior, asked each of them to reveal their ages. Junior’s parents decided to tell him, but in the form of a puzzle. Jack told Junior, “If you reverse the digits in my age, you get your mother’s age.
Jill told her son, “The sum of my age and your dad’s age is equal to 11 times the difference in our ages.”
“Wait a minute,” said Junior, “I can’t figure out your ages with just those two clues!”
“You’re right,” said Jack. “Remember that I am older than your mother.”
To solve this puzzle, we need to use the clues given by Jack and Jill.
1. Jack told Junior, "If you reverse the digits in my age, you get your mother's age."
Let's assume Jack's age is in the form of XY, where X is the tens digit and Y is the units digit. According to the clue, Jill's age should be in the form of YX. This means that Y must be greater than X since Jack is older than Jill. To find the digits X and Y, we can try different combinations of two-digit numbers and see if reversing the digits gives us the correct result.
2. Jill told her son, "The sum of my age and your dad's age is equal to 11 times the difference in our ages."
Let's suppose Jack's age is a and Jill's age is b. According to the clue, we can write the equation: a + b = 11 * (a - b). Simplifying this equation, we get: 12b = 10a. This implies that b = (5/6)a.
Let's now use these clues to find the possible ages of Jack and Jill:
Since Jack is older than Jill, let's assume Jack's age is in the form of XY, where X is the tens digit and Y is the units digit. We will try different combinations and see if it satisfies the given clues.
- Let's assume Jack's age is 21 (XY = 21).
Reversing the digits gives us 12, which is not equal to Jill's age in the form YX.
- Let's assume Jack's age is 32 (XY = 32).
Reversing the digits gives us 23, which is equal to Jill's age in the form YX.
Now, using the second clue, we can calculate Jill's age:
Jill's age (YX) + Jack's age (32) = 11 * (Jill's age (YX) - Jack's age (32))
YX + 32 = 11(YX - 32)
YX + 32 = 11YX - 352
10Y + 32 = 352
10Y = 320
Y = 32
Therefore, Jill's age is 23.
Hence, Jack is 32 years old and Jill is 23 years old.