SOLUTION: 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
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Question 504017: 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.”
What are the ages of Jack and Jill?
Organize and show all of your work.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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,
:
Let x = the 10s digit of Jacks age
Let y - the units digit
:
“If you reverse the digits in my age, you get your mother’s age.
J = 10x + y
M = 10y + x
:
Jill told her son, “The sum of my age and your dad’s age is equal to 11 times the difference in our ages.”
(10x+y) + (10y+x) = 11[(10x+y) - (10y+x)]
10x + x + y + 10y = 11(10x - x - 10y + y
11x + 11y = 11(9x - 9y)
simplify, divide both sides by 11
x + y = 9x - 9y
y + 9y = 9x - x
10y = 8x
simplify, divide both sides by 2
5y = 4x
y = x
the only integer solution: x=5, y=4
:
Jack is 54, Mom is 45
;
:
See if that works out in the statement:
"The sum of my age and your dad’s age is equal to 11 times the difference in our ages.”
54 + 45 = 11(54-45)
99 = 11(9)
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