Question 1170066
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Unlike the solution from the other tutor....<br>
(1) take the time to figure out how to set up the problem using a single variable; and
(2) interpret the given information correctly.<br>
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.<br>
The sum of their ages is 24:<br>
{{{(x)+(x+2)+(3x+8) = 24}}}<br>
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.<br>
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.<br>
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:<br>
Mike 1 --> Joe 1+2=3 --> Raymond 24-(1+3) = 20 but 3(3)+2 = 11<br>
Mike 2 --> Joe 2+2=4 --> Raymond 24-(2+4) = 18 but 3(4)+2 = 14<br>
Mike 3 --> Joe 3+2=5 --> Raymond 24-(3+5) = 16 but 3(5)+2 = 17<br>
That shows us there is no integer value for Mike's age that will satisfy the conditions of the problem.<br>