If a and b= 10.6 kilograms, a+c=8.5, and b+c= 6.1, what are a, b, and c

Question

It's an algebra question

Answer 1

You have 3 equations:

 

a + b = 10.6

a + c =8.5

b + c = 6.1

 

What you can do is subtract the first equation from the second equation like this:

 

        a + b = 10.6

     - (a + c = 8.5)

_________________

     0 + b - c = 2.1

 

(The zero is from a - a, the b is kept positive, and the c is now negative because we subtracted it).

 

So now the new equation is:

 

b - c = 2.1

 

Now we can add the third equation from the list at the top to this new one (we add because in the one at the top we have a +c, while in this new one we have a -c, so we can add them to eliminate c).

 

        b - c =2.1

    + b + c = 6.1

_______________

       2b + 0 = 8.2

 

And now we can solve for b:

 

2b = 8.2

b = 4.1

 

Now that we know b, we can solve for the other variables by plugging in 4.1 for b:

 

a + b = 10.6

a + (4.1) = 10.6

a = 6.5

 

b + c = 6.1

(4.1) + c = 6.1

c = 2

 

And if we would like to check, we can plug in a and c into the second equation from the list, now that we know them:

 

a + c = 8.5

(6.5) + (2) = 8.5

8.5 = 8.5

 

And we see that the numbers are correct.