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a+b=13 b+c=24 c+a=19 what is the value of a+b+c.

 Mar 24, 2020
 #1
avatar+1968 
+1

a+b=13

b+c=24

a+c=19.

 

Hint: Use the subtraction method to subtract the variables from one another. Once you know one, you know all!

 Mar 24, 2020
 #2
avatar+483 
+1

A simple and concise method is to add all 3 of these equations up. We don't have to subtract any of them to find individual variables. If we add all 3 of these, we get:

 

2a + 2b + 2c = 56

If we divide by 2(factor out 2) from both sides, we then get:

 

a + b + c = 28

 

See? Not so bad, was it?

 Mar 24, 2020
 #4
avatar+24978 
+1

a+b=13 b+c=24 c+a=19 what is the value of a+b+c.

 

\(\begin{array}{|lrcll|} \hline (1) & a+b=13 \\ (2) & b+c=24 \\ (3) & c+a=19 \\\\ (1)+(2)+(3): &(a+b)+(b+c)+(c+a) &=& 13+24+19 \\ & (a+b+c)+(a+b+c) &=& 13+24+19 \\ & 2(a+b+c) &=& 13+24+19 \\\\ & a+b+c &=& \dfrac{13+24+19}{2} \\\\ & a+b+c &=& \dfrac{56}{2} \\\\ & \mathbf{a+b+c} &=& \mathbf{28} \\ \hline \end{array}\)

 

laugh

 Mar 24, 2020

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