Question 1170066: Raymond, Joe, and Mike are brothers. Raymond is the oldest and Mike is the youngest. The sum of the ages of the 3 brothers is 24. The difference between Joe and Mike’s age is 2 years. Raymond’s age is 2 more than three times Josh’s age.
Find the age of each brother.
Found 3 solutions by josgarithmetic, greenestamps, MathTherapy:
Answer by josgarithmetic(39616)   (Show Source):
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
Unlike the solution from the other tutor....
(1) take the time to figure out how to set up the problem using a single variable; and
(2) interpret the given information correctly.
Mike is the youngest, so let x be Mike's age.
Joe's age is 2 more than Mike's, so x+2 is Joe's age.
Raymond's age is 2 more then 3 times Joe's age (not Josh's!), so Raymond's age is 3(x+2)+2 = 3x+8.
The sum of their ages is 24:
Trying to solve this using basic algebra gives a non-integer value. So, although the other tutor set up the equation incorrectly, they were correct in saying that something is wrong with the statement of the problem.
It is easy to verify that there is no solution informally; in fact, given a problem like this without the need for a formal algebraic solution, an informal solution would be much faster.
Using the information that Joe is 2 years older than Mike and that the sum of the three ages is 24, look for a combination that makes Raymond's age 2 more than 3 times Joe's age:
Mike 1 --> Joe 1+2=3 --> Raymond 24-(1+3) = 20 but 3(3)+2 = 11
Mike 2 --> Joe 2+2=4 --> Raymond 24-(2+4) = 18 but 3(4)+2 = 14
Mike 3 --> Joe 3+2=5 --> Raymond 24-(3+5) = 16 but 3(5)+2 = 17
That shows us there is no integer value for Mike's age that will satisfy the conditions of the problem.
Answer by MathTherapy(10551)  (Show Source):
You can put this solution on YOUR website! Raymond, Joe, and Mike are brothers. Raymond is the oldest and Mike is the youngest. The sum of the ages of the 3 brothers is 24. The difference between Joe and Mike’s age is 2 years. Raymond’s age is 2 more than three times Josh’s age.
Find the age of each brother.
As stated by the tutor, there are no INTEGER values for the ages, and as you might be aware, age is supposed to be an INTEGER.
Regarding the other person who responded, I do believe you MUST realize that his so called "answers" are nothing but rubbish!!
Let me point out something that you may have noticed. It was given that, ".....The sum of the ages of the 3 brothers is 24." These are the ages, according to him:
 -------Joe
 ------Raymond
 -------Mike
Where in this world would one find that the sum of 4, 14, and 2 is 24? If you know, please let me know!!
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