Question 1186009: 1. The product of the ages, in years, of three teenagers is 4590. None of the teens are the same age. What are the ages of the teenagers?
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Found 3 solutions by Theo, ikleyn, Alan3354:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the product of the angles is 4590.
the possible ages are:
13, 14, 15, 16, 17, 18, 19
i tried 14 * 15 * 16 = 3360 - too small
i tried 15 * 16 * 17 = 4080 - still too small
i tried 16 * 17 * 18 = 4896 - too large
i tried 15 * 17 * 18 = 4590 - got it !!!!!
another possible way.
15^3 = 3375 - too small
16^3 = 4096 - too small
17^3 = 4913 - too large
the numbers can't all be 17 or greater.
the numbers can't all be 16 or less.
15 * 16 * 17 = 4080 - too small
16 * 17 * 18 = 4896 - too large
15 * 17 * 18 = 4590 - right on.
it's a process of narrowing down the possible values.
the method used above is just one of many possible methods.
Answer by ikleyn(52786)  (Show Source):
You can put this solution on YOUR website! .
The product of the ages, in years, of three teenagers is 4590. None of the teens are the same age.
What are the ages of the teenagers?
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They want you present the number 4590 as the product of three positive integer different numbers
from the interval 13 to 19 inclusive.
Start finding prime divisors of the number 4590.
It is not so difficult as it may seem at the beginning.
First, there is a factor 10, which is the product of 2 and 5.
Divided by 10, the number 4590 gives the quotient 459.
The number 459 has the sum of the digits 4+5+9 = 18, which is divisible by 9.
So, according to the divisibility by 9 rule, the number 459 is divisible by 9 = 3*3.
The quotient is 459/9 = 51.
Next, 51 = 17*3.
+---------------------------------------------+
| Thus 4590 = 10 * 9 * 17*3 = 2*5*3^3*17. |
+---------------------------------------------+
17 is one of the targeted factors.
Next, it is obvious that the other targeted factor is 3*5 = 15.
The remaining factor is  = 18.
So, we just found the answer in this way: 4590 = 15*17*18.
CHECK. 15*17*18 = 4590. ! Correct !
Solved.
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Answer by Alan3354(69443)  (Show Source):
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