# Thread: Word Age Problems - confusing question

1. ## Word Age Problems - confusing question

I need help understanding the final answer. If the answer is the ages they are now, why do we need to know the sum of their ages in 2 years? Confusing.
Thanks.

Mike is 4 years older than Ron. In two years, the sum of their ages will be 84. How old are they now?

R=Ron’s age now
R+4=Mike’s age now
R+2+R+4+2 =84
2R+8 =84
2R+8-8=84-8
2R=76
R=38

Ron is 38. Mike is 42.

2. ## Re: Word Age Problems - confusing question

Originally Posted by falcios
I need help understanding the final answer. If the answer is the ages they are now, why do we need to know the sum of their ages in 2 years? Confusing.
Thanks.

Mike is 4 years older than Ron. In two years, the sum of their ages will be 84. How old are they now?
because this is what the problem tells you.

It says in 2 years the sum of their ages will be 84. Not today.

$(m+2)+(r+2)=84$

$(r+4+2)+(r+2) = 84$

$2r + 8 = 84$

$2r = 76$

$r = 38$

$m = 38+4 = 42$

3. ## Re: Word Age Problems - confusing question

Originally Posted by falcios
Mike is 4 years older than Ron. In two years, the sum of their ages will be 84. How old are they now?
R+4=Mike’s age now
R+2+R+4+2 =84
2R+8 =84
2R+8-8=84-8
2R=76
R=38
Ron is 38. Mike is 42.
Maybe a different format will make it clear?
$M&=R+4\\&\text{Now in two more years, add their ages.}\\(M+2)+(R+2)&=84\\([R+4]+2)+(R+2)&=84\\2R+8=84 \\\text{ }\vdots$

4. ## Re: Word Age Problems - confusing question

In algebra, a central idea is that knowing some arithmetic facts about a set of numbers lets us determine what numbers make up the set. What the numbers represent is irrelevant to finding the numbers.

You are asked to find the current ages of two people, measured in number of years. You are given arithmetic facts about their ages today and about their ages two years from today. You are also expected to know an arithmetic fact about the relationship between ages today and two years from today. We do not need to know anything more than those arithmetic facts to find out what we want to know.

The psychological issue is this. There are four numbers involved, representing current and future ages of two people. Our facts concern all four numbers, and our method of solution requires all four. But we want to know about just two of them. In other words, the information that we need is greater than the information that we want.

5. ## Re: Word Age Problems - confusing question

Originally Posted by falcios
If the answer is the ages they are now, why do we need to know the sum of their ages in 2 years? Confusing.
To answer a question with a question:
can you solve the problem without that information?

6. ## Re: Word Age Problems - confusing question

The answer is a simple principle. You need to solve for two variables; Mike's age (X) and Ron's age (Y) so you need two equations:

X = Y + 4

(x + 2) + (y + 2) = 84

Steve