Thread: The average of A and B is 2.5...

The average of A and B is 2.5, the average of B and C is 3.8, and the average of A and C is 3.1. Fin A, B, and C.

Originally Posted by ceasar_19134

The average of A and B is 2.5, the average of B and C is 3.8, and the average of A and C is 3.1. Fin A, B, and C.

if the average of A and B is 2.5, then

(A + B)/2 = 2.5
=> A + B = 5

if the average of B and C is 3.8, then
(B + C)/2 = 3.8
=> B + C = 7.6

if the average of A and C is 3.1, then
(A + C)/2 = 3.1
=> A + C = 6.2

thus we have three simultaneous equations:

A + B = 5 ......................(1)
B + C = 7.6 ....................(2)
A + C = 6.2 ....................(3)

subtract eqaution (1) from (3), we get:

C - B = 1.2 ..............(4) = (3) - (1)
B + C = 7.6 ...............(2)

add these two equations, we get:
2C = 8.8
so C = 4.4

but A + C = 6.2 ...............(3)
so A + 4.4 = 6.2
so A = 6.2 - 4.4 = 1.8

but A + B = 5 ..................(1)
so 1.8 + B = 5
so B = 5 - 1.8 = 3.2

so we have
A = 1.8, B = 3.2, and C = 4.4

Originally Posted by ceasar_19134

The average of A and B is 2.5, the average of B and C is 3.8, and the average of A and C is 3.1. Fin A, B, and C.

1. A+B=5

2. B+C=7.6

3. A+C=6.2

Equation 3 minus equation 1 gives:

4. C-B=1.2

Equation 2 plus equation 4 gives:

5. 2C=8.8

So C=4.4, substitute this into 3 gives A=1.8, and into 2 gives B=3.2

RonL

Hello, ceasar_19134!

I found another method . . . It's kind of devious and I don't recommend it.
. . But I thought I'd show it to you anyway.

The average of A and B is 2.5, the average of B and C is 3.8,
and the average of A and C is 3.1. . Find A, B, and C.

We have: .½(A + B) .= .2.5 . → . A + B .= .5.0 .[1]
. . . . . . . .½(B + C) .= .3.8 . → . B + C .= .7.6 .[2]
. . . . . . . .½(A + C) .= .3,1 . → . A + C .= .6.2 .[3]

Add the three equations: .2A + 2B + 2C .= .18.8 . → . A + B + C .= .9.4 .[4]


Subtract [1] from [4]: .A + B + C .= .9.4
. . . . . . . . - - - . . . . .A + B . - . .= .5.0
and we get: .C = 4.4


Subtract [2] from [4]: .A + B + C .= .9.4
. . . . . . . . - - . . . . . . . . .B + C .= .7.6
and we get: .A = 1.8


Subtract [3] from [4]: .A + B + C .= .9.4
. . . . - . . - - . . . . . . .A . .+ . .C .= .6.2
and we get: .B = 3.2