X is two times of Y, while Z is 16 ⅔% more than Y and U is 20% more than average of X, Y & Z. If difference between X & U is 240, then find the average of X & U?
Question
X is two times of Y, while Z is 16 ⅔% more than Y and U is 20% more than average of X, Y & Z. If difference between X & U is 240, then find the average of X & U?
Solution
Sure, let's solve the problem step by step:
Step 1: Let's assign variables to the given information:
- X: Represents a value that is two times Y.
- Y: Represents a certain value.
- Z: Represents a value that is 16 ⅔% more than Y.
- U: Represents a value that is 20% more than the average of X, Y, and Z.
Step 2: Express the given information in terms of equations:
- X = 2Y
- Z = Y + (16 ⅔%)Y = Y + (50/3)Y = (53/3)Y
- U = 1.2 * (average of X, Y, and Z)
Step 3: Find the average of X and U:
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We are given that the difference between X and U is 240. So, we can write the equation: X - U = 240
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Substitute the values of X and U from the equations above: 2Y - 1.2 * (average of X, Y, and Z) = 240
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Substitute the values of X and Z in terms of Y: 2Y - 1.2 * ((2Y + Y + (53/3)Y)/3) = 240
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Simplify the equation: 2Y - (2.4/3) * (6Y + (53/3)Y) = 240
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Solve for Y: 2Y - (2.4/3) * (18Y + 53Y/3) = 240 2Y - (2.4/3) * (54Y/3 + 53Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/3) = 240 2Y - (2.4/3) * (107Y/
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