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Three different numbers are given. The average of

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Tags: MATH

RASTA aktiv_icon

21:06 Uhr, 02.12.2022

Tag alles!

Three different numbers are given.
The average of the average of the two smaller numbers and the average of the two larger numbers is equal to the average of all three numbers.
The average of the smallest and largest numbers is

2022

.
Determine the sum of the three given numbers.

the teacher told me I could go this way, but I don't get it.
Could you clear this for me, please, thanks in advance.
see attachement

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atarca aktiv_icon

22:31 Uhr, 02.12.2022

The hint is wrong. You have to plug

[2]

into the left hand side.

calc007

22:34 Uhr, 02.12.2022

Yes, all right.
So now, I'd suggest to start simplifying the formulas.
How about your trials, how about your progress?

I guess, you'll be able to show up the value of

' b' . .

Respon

13:23 Uhr, 03.12.2022

Determine the sum of the three given numbers.
Rearrange until you have

a + b + c = f (a, c)

. You should be able to plug

\frac{a + c}{2} = 2022

into the RIGHTHAND side and solve for

a + b + c

.
Let's do so !

\frac{1}{2} \cdot (\frac{a + b}{2} + \frac{b + c}{2}) = \frac{a + b + c}{3}

\frac{1}{2} \cdot (\frac{(a + b + c) + b}{2}) = \frac{a + b + c}{3}

| \cdot 12

3 \cdot (a + b + c) + 3 \cdot b = 4 \cdot (a + b + c)

b = a + b + c - (a + c)

3 \cdot (a + b + c) + 3 \cdot (a + b + c) - 3 \cdot (a + c) = 4 \cdot (a + b + c)

2 \cdot (a + b + c) = 3 \cdot (a + c)

a + b + c = \frac{3}{2} \cdot (a + c)

\frac{a + c}{2} = 2022 \Rightarrow a + b + c = 3 \cdot 2022 = . .

Respon

10:10 Uhr, 04.12.2022

Oder kürzer ( siehe calc007

) :

\frac{1}{2} \cdot (\frac{a + b}{2} + \frac{b + c}{2}) = \frac{a + b + c}{3}

\frac{a + 2 \cdot b + c}{4} = \frac{a + b + c}{3}

\frac{a + c}{4} + \frac{b}{2} = \frac{a + c}{3} + \frac{b}{3}

| \cdot 12

3 \cdot (a + c) + 6 \cdot b = 4 \cdot (a + c) + 4 \cdot b

b = \frac{a + c}{2}

\Rightarrow

a + b + c = a + \frac{a + c}{2} + c = \frac{3}{2} \cdot (a + c)

RASTA aktiv_icon

18:06 Uhr, 04.12.2022

thanks a lot.
Vielen Dank.
Verzeihen Sie mir, dass ich zu spät auf Ihre Beiträge geantwortet habe. Ich war mit einer anderen Aufgabe beschäftigt.

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