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Analytic Geometry problem: How do you find 3 numbers in a question without knowing what the numbers are?

• Hey Guys! We are right now doing Analytic Geometry in math, but were suppose to do these questions for Homework where you try and find the solution for three unknown answers. It gives me options of what the answers could be so I will let you guys see that after the question, if it helps. o_0 Here is the math question: The second of the three numbers is 8 more than the first, and the third number is 3 less than 3 times the first. If the third number is 15 more than the second, find the three numbers. 1? 2? 3? There it is. Here are the possible answers for the three numbers: 14, 22, 37, 13, 21, 36, 14, 9, 29, 17, 12, 37 If anyone can figure this out it will be greatly appreciated. And also when it says the second number of three numbers is 8 more than the first, does that mean the second number could be 8 if the first was 0? Thanks :)

• Answer:

  The solution is 13 21 36 When it says the second number of three numbers is 8 more than the first, does that mean the second number could be 8 if the first was 0? YES IT DOES - It "HAS" to be 8 IF the first number was 0 (not could). However that does not apply in your above problem. First things first take the first set of numbers 14 22 37 The second of the numbers (22) is 8 more than the first (14) TRUE The third number (37) is 3 less than three times the first (3*14 = 42, then - 3 = 39) As 37 is not 39 you can REJECT this permutation of numbers Take 14 9 29 The second (9) is 8 more than the first (14) FALSE it is less than the first therefore REJECT this permutation of numbers Take 17 12 37 Once again the second number is less than the first therefore REJECT this permutation This only leaves 13 21 36 The second number is 8 more than the first: 21 is 8 more than 13 = TRUE The third number is 3 less than 3 times the first 36 = (3*13) - 3 = 39 -3 = 36 = TRUE The third number is 15 more than the second: 36 = 21 + 15 + TRUE Therefore as all three criteria are true - the answer is 13, 21, 36