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Question POOLE
Homework Progress
729
Five whole numbers are written in order
4 6 x y
10
The mean and median of the five numbers are the same.
Work out the values of x and y.

Sagot :

MrRoyal

Answer:

[tex]x = 7[/tex] and [tex]y = 8[/tex]

Step-by-step explanation:

Given

4 6 x y 10

Median = Mean

Required

Find x and y

The mean is calculated as:

[tex]Mean=\frac{4 + 6 + x + y + 10}{5}[/tex]

Collect Like Terms

[tex]Mean=\frac{4 + 6 + 10+ x + y }{5}[/tex]

[tex]Mean=\frac{20+ x + y }{5}[/tex]

The median which is the mid-data is x

i.e.

[tex]Median = x[/tex]

Median = Mean; so, we have:

[tex]x=\frac{20+ x + y }{5}[/tex]

Multiply through by 5

[tex]5 * x=\frac{20+ x + y }{5} * 5[/tex]

[tex]5 x=20+ x + y[/tex]

Collect Like Terms

[tex]5 x - x=20+ y[/tex]

[tex]4x=20+ y[/tex]

Since the numbers are in order, the values of x and y could be any of 7, 8 and 9

Such that:

[tex]x < y[/tex]

So, we need to test the equation with these values

Let x = 7

So, we have:

[tex]4x=20+ y[/tex]

[tex]4 * 7 = 20 + y[/tex]

[tex]28 = 20 + y[/tex]

[tex]28 - 20 = y[/tex]

[tex]8 = y[/tex]

[tex]y = 8[/tex]

This is true for the equation.

Hence:

[tex]x = 7[/tex] and [tex]y = 8[/tex]

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