SOLUTION: Mary is thress times as old as her son. in 12 years, marys age will be 1 year less than twice her son's age. how old is each now

Question 143421: Mary is thress times as old as her son. in 12 years, marys age will be 1 year less than twice her son's age. how old is each now
Answer by zephyr(9) (Show Source): You can put this solution on YOUR website!
Okay. So first, pretend that M=Mary's age, and S= Mary's Son's age.

now, if Mary is 3 times as old as her son. Then if her son was 3 times as old, he would be the same age as Mary, right? Now if we put that into an equation. that would look like

Now moving on. To put the rest of the problem into an equation, it would look like this.

First of all, the S+12 is in parentheses because IN twelve years if the son was twice his age, then mary would be one year younger. It's not "if her son was twice his age, and grew 12 years older".
Second of all, there is a -1 because if he was a year younger after he grew 12 years younger and multiplied his age by 2, he would be Mary's age.

But now it's time to substitute. Remember the equation from earlier? (3S=M) We're going to substitute that for M. So now the equation looks like this.

Now let's work that through.

Now subtract 2S from each side

So that's the son's age.

Now, if you wanted, you could do this whole thing over to find out Mary's age (just use 1/3M=S). But wouldn't it be easier if we just substituted 23 for the son's age? (In the equation ) Yep. So let's do that now.

And there you have it! But just to check, you can substitute 23 for the son's age and 69 for mary's age in the equation we used earlier, (). So let's do that now.

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