# Mr. P is 76, and his granddaughter is 12.  In how many years will Mr. P. be 5 times as old as his granddaughter?  Thank you!?

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Let n be the number of years until that happens.

Mr. P's age will be 76 + n

His granddaughter will be 12 + n

You want the first amount to be 5 times the second amount:

76 + n = 5(12 + n)

Distribute:

76 + n = 60 + 5n

Subtract 60 from both sides and also subtract n from both sides:

76 - 60 = 5n - n

16 = 4n

Divide both sides by 4 to isolate n:

n = 16/4

n = 4

In 4 years, Mr. P will be 80

In 4 years, his granddaughter will be 16

5 * 16 = 80

This will happen in 4 years

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• I feel old            .

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• @Puzzling's answer is excellent, as usual.

Just for fun, here is how I thought about it, without using pencil and paper.

Mr. P is so old, that adding a few years to his age isn't going to change his age much.  His grandaughter is young, however, so any additions to her age matter a lot, in finding the ratio of their ages.  So I'm going to divide Mr. P's current age by 5 to find out approximately how old his granddaughter would need to be.  76 isn't evenly divisible by 5, so I'll go with 75, which is.  75/5 = 15, so that's my first guess.  3 years from now, his granddaughter will be 15.  But if I add 3 to 76, the answer isn't a multiple of 5.  So I'll try adding 4, and by luck, that works out.  My next guess would have been adding 9, and if that didn't work, I'd go back to pencil and paper.

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• 5 x 16 = 80, so I will guess 4 {If he is not dead.}

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• let x number of years that MR. P  be 5 times as his granddaughter.

76 + x = 5(x + 12)

76 + x = 5x + 60

x - 5x = 60 - 76

-4x = - 16

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• LET THE NO OF YEARS TAKEN FOR MR P TO BECOME 5 TIMES HIS GRANDDAUGHTER'S AGE BE  X YEARS

(76 +X) / (12 +X) =  5/1

CROSS MULTIPLY

5 (12 +X) = 76 +X

5X -X = 16

4X =16

CHECK

76+4 = 80

12+4 =16

80/16 = 5

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• Solve for n:

76+n = 5(12+n)

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• Mr. P is 76, and his granddaughter is 12.

x : y = 76 : 12 = 19 : 3

(x + 4) : (y + 4) = 5 : 1

Mr. P. will be 5 times as old as his granddaughter

in another 4 years.

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• In n years, Mr. P will be (76+n) years old and his granddaughter will be (12+n) years old.  If at that time, he is five times as old as her, you can write that as:

76 + n = 5(12 + n)

76 + n = (5)(12) + 5n                   Use the distributive property a(b+c) = ab+ac

76 + n = 60 + 5n                          Simplify

16 + n = 5n                                  Subtract 60 from both sides

16      = 4n                                  Subtract n from both sides

4      =  n                                   Divide both sides by 4

So, that will happen in 4 years.

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• 76 + x = 5(12+ x)

==> 76 + x = 60 + 5x

==> 16 = 4x

==> x = 4

So, in four years, he's be 5 times as old as his granddaughter

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