The father is thrice as old as his son. 10 years ago the fathers age was 5.5 times the son's age. Determine the present age of the father.
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Answer:
Answering this without algebra will be tricky. But let’s try.
Six years ago, the son had a particular age, and his father was four times that age. (In algebra, we’d say that the son’s age six years ago was X, and his father’s age then was 4X. But we said we’d try to avoid algebra.)
Now, six years later, the son is six years older (X+6), and so is the father (4X+6). We’re told that now the father is only three times as old as his son. That means that three times the son’s age — 3(X+6), or 3X+18 — is the same as the father’s age now (4X+6). That means that 3X+18 = 4X+6… which is the same as saying that 3X+12 = 4X. Intuitively, we know what that means — you need to add 12 to 3X to make it 4X, which means that X=12.
X was the son’s age six years ago. So six years ago, the son was twelve and the father was forty-eight. Six years later (today), the son is eighteen and the father is fifty-four. (It works — the father is three times his son’s age now!)
But the question is: what will the ratio of their ages be in another six years? Well, six years from now, the son will be twenty-four, and the father will be sixty. What ratio is that? That’s 60/24, which we can reduce to 10/4, or 5/2, or two and a half.
As you can see, we tried to do this without using algebra. That didn’t work out too well; sorry.
By the way, one of the hardest parts, for beginning algebra students, is deciding what the variables should be. I could have set X to be anything — the son’s age now, the father’s age now, and so forth. I should have gotten the same answer regardless; the only difference is whether the arithmetic is easier or harder.
I chose to let the son’s age, six years ago, be X… because then I’d have to deal with addition and multiplication, which is generally easier than subtraction and division. But try it the other way, and see if you get the same answer! (You should!)
I hope it will be helpful to you friend
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