Question

I need help! Can u help me?

Answer 1

From clue 3, we know that the three numbers average to 15. This means we add up the three numbers x,y and z and divide by 3 to get 15. So one equation is (x+y+z)/3 = 15 which turns into x+y+z = 45 after multiplying both sides by 3.

Let's say that x < y < z. In other words x is the smallest number, y is the middle and z is the largest. Based on clue 2, this would tell us that z = 8*x (since largest is 8 times the smallest). We can replace the 'z' in the equation x+y+z = 45 with 8x like so

x+y+z = 45

x+y+8x = 45 ... replace z with 8x

9x+y = 45

Now onto clue #1. The smallest number x is a prime number and it is 1/6 times the size of the middle number y. Put another way, the middle number y is 6 times larger than the smallest number. We have this equation y = 6*x

9x+y = 45

9x+6x = 45 ... replace ywith 6x

15x = 45

x = 45/15

x = 3 which is a prime number

Now that we know x = 3, we can use it to find y

y = 6*x = 6*3 = 18

and then use x = 3 to find z

z = 8*x = 8*3 = 24

Therefore the three mystery numbers are 3, 18, and 24. Note how these three values add to 3+18+24 = 45 which you then divide over 3 to get 45/3 = 15. So the average of the values 3, 18, 24 is the number 15. This helps confirm the answer.