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Question 1111032: Malcolm’s mother is 27 years older than he is and their ages are both two-digit numbers. If Malcolm swaps the digits in his age, he gets his mother’s age.
a How old is Malcolm if the sum of the digits in his age is 5?
b What is the relationship between the digits in Malcolm’s age if the sum of the digits is
unknown.
c If the sum of the digits in Malcolm’s two-digit age is unknown, how many possible ages
could he be? What are these ages?
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Malcolm’s mother is 27 years older than he is and their ages are both two-digit numbers. If Malcolm swaps the digits in his age, he gets his mother’s age.
a How old is Malcolm if the sum of the digits in his age is 5?
b What is the relationship between the digits in Malcolm’s age if the sum of the digits is
unknown.
c If the sum of the digits in Malcolm’s two-digit age is unknown, how many possible ages
could he be? What are these ages?
let Malcolm's age be 10x+y
mothers age is 10x+y+27
equation after swapping the digits
10y+x = 10x+y+27
9y-9x=27
y-x=3
x+y=5
add the equations
2y=8
y=4
therefore x= 1
Malcom's age = 10x +y = 14
mother's age = 14+27 = 41
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