Two gears have a total of 89 teeth. One has 4 less than twice the number of teeth the other gear has. How many teeth do each gear have?

Question

Two meshing gears in a printer have a total of 89 teeth. One of the gears has 4 teeth less than twice the number of teeth of the other gear. How many teeth does each gear have?

Answer 1

Let's call the gears x and y.

Here's what we know:

x + y = 89

y = 2x - 4

 

Since we have a value for y, we can put that into our equation:

x + (2x - 4) = 89

Simplify:

3x - 4 = 89

Now we isolate x. Add 4 to both sides:

3x = 93

And now divide both sides by 3:

x = 31 teeth

 

Now that we know x, we can solve for y:

y = 2 * 31 - 4

y = 62 - 4

y = 58 teeth

 

Now we check our answer by going back to our original question:

31 + 58 = 89

89 = 89

 

Answer 2

If x be the no of teeth for one gear, the no of teeth for the other gear is 2x-4

 

So x+ 2x-4 = 89

3x -4=89

3x= 89+4 =93

x= 93/3 = 31

So the no of teeths for the gears are 31 and 2x31-4 or 58