If a+b=c-10 & a+b+c=35 then what is the value of a & what is the value of b?

Question

This is a logical reasoning question.

Answer 1

a+b=c-10     [eq1]

a+b+c=35    [eq2]

 

a+b =  c  - 10     [eq1]
a+b = -c + 35    [modified eq2]

-----------------

2a+2b = 25        [add equations]

 a + b = 12.5      [divide both sides by 2]

 

There are an infinite number of allowable values for a and b, as long as their sum is 12.5 [note: c will always equal 22.5].

  

Answer 2

Hi Chiradeep, given the two equations, we can find the value of c. Once we know the value of c, we can find values for a and b.

 

a + b = c - 10

 

a + b + c = 35

 

Put the two equations in the same format.

 

a + b - c = -10

 

a + b + c = 35

-----------------

 

Multiply the second equation by -1 and add:

 

 a + b - c = -10

-a - b  - c = -35

----------------------

         -2c = -45

 

Divide both sides by -2:

 

c = 22.5

 

Returning to the two equations:

 

a + b = c - 10

----------------

 

a + b = 22.5 - 10

 

a + b = 12.5

 

============

 

a + b + c = 35

-----------------

 

a + b + 22.5 = 35

 

a + b = 35 - 22.5

 

a + b = 12.5

 

This shows there is an infinite set of solutions for a and b.

 

If we solve a + b = 12.5, for b: b = 12.5 - a

 

Pick any value for a, say 10, then b will equal 2.5. Try other combinations, they are all valid.

 

Questions?

Answer 3

If

a + b - c = -10

a + b + c = 35

then 2c = 45, or c = 22.5

Answer 4

a + b = c - 10

a + b + c = 35

 

a + b - c = -10

a + b - c =  35

-------------------

2a + 2b = 25

 

2b = -2a + 25

b = (-2a + 25)/2

b = -a + 12.5

 

2a = -2b + 25

a = -b + 12.5