SOLUTION: Bob Hope was born 2 years after Clark Gable and 2 years before Henry Fonda (Doubleday Almanac). In 1951, after all three of them had their Birthdays, the sum of their ages was 1

Question 203653: Bob Hope was born 2 years after Clark
Gable and 2 years before Henry Fonda (Doubleday
Almanac). In 1951, after all three of them had their
Birthdays, the sum of their ages was 144. In what year were they born?

Answer by PRMath(133) (Show Source): You can put this solution on YOUR website!
OK, here goes:

Bob Hope we'll call "B"
Clark Gable we'll call "C"
Henry Fonda we'll call "H"

Soo.....

Bob is 2 years younger than Clark so in other words,
Clark is 2 years older than Bob, which we would write as: C = B + 2

Bob = 2 years older than Henry so in other words,
Henry is 2 years younger than Bob, which we would write as: H = B - 2.

Now in 1951, their ages added up to be: 144 years. We would say........

B + H + C = 144 BUT that is THREE variables. Let's use substitution and change the equation.

We know from above that C = B + 2.
We know from above that H = B - 2.
Now let's substitute:

B + H + C = 144
B + B - 2 + B + 2 = 144 (See how we substituted in the info for H and C?)
3B = 144 (We combined like terms. B + B + B = 3B. -2 + 2 = 0)
= (Divided both sides by 3 to isolate "B")
B = 48.

SO we know that in 1951, Bob was 48 years old.
Bob is two years younger than Clark, so Clark must have been 50 in 1951.
Henry is two years younger than Bob, so Henry must have been 46 in 1951.

Let's check. Does ? YES! :-) But we're not done!

When were they born? Well those were their ages in 1951, so let's subtract all those ages from 1951 to see when they were born.............

1951 - 48 = 1903 (BOB)
1951 - 50 = 1901 (CLARK)
1951 - 46 = 1905 (HENRY)

AND... if you need a further check, just go to internet movie database. :-)

Anyway, these three years check out with math (and ok, with imdb, too).

I hope this helps you. :-)

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