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There are 3 different whole numbers X, Y and Z. The average of these numbers is 90. The quotient is 7, when you divide X by Y. What is the smallest possible value of Z?

Question

There are 3 different whole numbers X, Y and Z. The average of these numbers is 90. The quotient is 7, when you divide X by Y. What is the smallest possible value of Z?

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Solution

Step 1: Understand the problem We are given that X, Y, and Z are three different whole numbers. Their average is 90, which means the sum of these three numbers is 270 (since 90*3 = 270). We are also given that X/Y = 7. We are asked to find the smallest possible value of Z.

Step 2: Formulate the equations From the problem, we can formulate two equations:

  1. X + Y + Z = 270 (since the sum of the numbers is 270)
  2. X = 7Y (since X/Y = 7)

Step 3: Substitute the second equation into the first one Substituting X = 7Y into the first equation, we get: 7Y + Y + Z = 270 8Y + Z = 270

Step 4: Find the smallest possible value of Z Since X, Y, and Z are whole numbers, Y must be a whole number. The smallest whole number Y that satisfies the equation 8Y + Z = 270 is 1. Substituting Y = 1 into the equation, we get: 8*1 + Z = 270 Z = 270 - 8 Z = 262

So, the smallest possible value of Z is 262.

This problem has been solved

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