Algebra word problem

Question

ge and ibm had combined profits of 24.3 billion ge made 8 billion dollars more than ib. What did they both make?

Answer 1

This word problem is kind of tricky.

 

Let's say that the profit of GE is the symbol G and the profit of IBM is the symbol M.

 

The first part of the sentence says that GE and IBM made a total profit of 24.3 billion. In math language, that means

 

G + M = 24.3

 

The second part says that GE made 8 billion more than IBM. If GE made more that IBM, that should tell you that G > M. Specifically that

 

G + 8 = M

 

Now we have 2 equations and 2 unknowns. You can solve this a number of ways, but subtracting the equations is probably what you learned in class.

 

     G  + M       = 24.3

- ( G  +       8  =            M)

            M  - 8 = 24.3 -  M

 

Notice how the G variable cancels out when you do this? That is excellent because now we have an equation with only 1 unknown.

 

M - 8 = 24.3 - M

 

Now we group like terms. That means adding M to both sides to get

 

M + M - 8 = 24.3

 

Add 8 to both sides to get (also M + M = 2M)

 

2M = 32.3

 

Divide both sides by 2 to get

 

M = 16.15

 

Now we plug that back into either one of the original equations to find G. Let's pick

 

G + 8 = M

 

subtract 8 from both sides

 

G = M - 8

 

now substitute what we had for M back in

 

G = 16.15 - 8

 

G = 8.15

 

Let's check these answers to confirm

 

G + 8 = M

 

8.15 + 8 = 16.15

 

M = 16.15

 

And our answer checks out. I hope this helps! Please ask if you have a question about any of the steps involved.