SOLUTION: if a b=10 b c=20 c a=24 how much is a, b and c and how

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Question 821474: if
a b=10
b c=20
c a=24
how much is a, b and c
and how
Found 2 solutions by ortarico, Alan3354:
Answer by ortarico(23) (Show Source):
You can put this solution on YOUR website!
if
a b=10
b c=20
c a=24
how much is a, b and c
and how
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a b = 10 ---- eqn1
b c = 20 ---- eqn2
c a = 24 ---- eqn3
--------
from eqn1: a b = 10,
a = 10 - b ---- eqn4
from eqn3: c a = 24,
a = 24 - c ---- eqn5
-----------
equating eqn4 and eqn5:
10 - b = 24 - c
b - c = -14 ---- eqn6
-----------
bringing eqn2 and eqn6:
b c = 20
b - c = -14
:. 2b = 6
b = 3
----------
substituting b = 3 in eqn1
a b = 10
a 3 = 10
a = 7
----------------
substituting a = 7 in eqn3:
c a = 24
c 7 = 24
c = 17
-------------------
:. a = 7, b = 3 and c = 17

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
if
a b=10
b c=20
c a=24
----------
Use * for multiply, or don't put a space
---
ab=10
bc=20
ca=24
-----------
a = 10/b
Sub for a in eqn 3
10c/b = 24
---
bc = 20 --> c = 20/b
10c = 24b
200/b = 24b
b^2 = 200/24 = 25/3

-----------
a = 10/b

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c = 24/a