Step-by-step explanation:
If a+b=8, b+c=10 and c+a=12, what is the value of a+b+c?
a+b+c=15
(a+b)+(b+c)+(c+a)=8+10+12
⟹2(a+b+c)=30
a+b+c=15
(a+b+c)−(b+c)=15−10
a=5⟹b=3⟹c=7
5+3+7=15
Proof:
5+3=8✓
3+7=10✓
7+5=12✓
Q.E.D.
Q. If a+b=8, b+c=10 and c+a=12, what is the value of a+b+c?
Find the value of a+b+c?
The quickest way is to add the given equations together :
Given. #1. a+b=8,
Given. #2. b+c=10
Given. #3. c+a=12
>> (a+b) + (b +c) +(c +a) = (8 + 10 + 12)
>> (2a + 2b + 2c) = 30
Answer. (a + b + c) = 15.
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The answer may be checked using elimination.
#1. a+b=8,
#2. b+c=10
#3. c+a=12
From. #2. - #1. >> #4. c - a = 2.
From. #4 + #3. >> #5. 2c = 14 >> c = 7.
From. #5. put c = 7 into #2 >> b = 10 - 7 = 3
Hence : a = 5; b = 3; c = 7.
Answer : ( a + b + c ) = 15
Agreed and checked.
