SOLUTION: John's age plus Mary's age is 59 years. The difference in their ages is 33 years. Can you tell the age for each one? Why or why not? If you ALSO know that John is younger than Mary

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Question 253433: John's age plus Mary's age is 59 years. The difference in their ages is 33 years. Can you tell the age for each one? Why or why not? If you ALSO know that John is younger than Mary, what are their ages?
Found 2 solutions by Theo, richwmiller:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
j = john's age
m = mary's age

j+m = 59

if john is older than mary, then:

j-m = 33

from this second equation we can solve for j in terms of m to get:
j = m + 33

we can substitute this in the first equation to get:

j + m = 59 becomes (m+33) + m = 59 which becomes 2m+33 = 59.

subtract 33 from both sides of this equation to get:

2m = 59-33 = 26

divide both sides of this equation by 2 to get m = 13

since j = m + 33, this means that j = 46

46 + 13 = 59

john is 46
mary is 13

we could only do this because we knew that john was older than mary.

if mary was older than john, then the results would be reversed.

just knowing the difference in the ages wasn't enough.

we had to know who was older.

Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
j+m=59
j-m=33
add
2j=92
j=46
m=13
m+j=59
m-j=33
2m=92
m=46
j=13
We can only tell the ages are 59 and 13 but not who is 59 and who is 13
If john is the younger then he is 13 and mary is 46