"Than" is the Man

Word questions in Algebra. 4 words to...

...scare anyone. However, there is hope...

Remember, "than" is the man. "Than" is the key to solving these questions. For example...

3 numbers add up to 180. The smallest is 20 less than the largest. The third is 10 more than the smallest. Name the three numbers.

These numbers are referenced against the other numbers. The word "than" helps us here. I see the word "smallest" appear twice, so I am going to use that as my reference, or "x". The word that appears the most should become your reference.

So...

...       if...

...the smallest is 20 less than the largest, then the largest must be 20 more than the smallest, 
or x + 20. We now have...

1) The smallest = x
2) The largest = x + 20

We just need the third number.

The third is 10 more than the smallest. The smallest = x, so the third number must be x + 10.

We now have...

1) The smallest = x
2) The largest = x + 20
3) The third number = x + 10.

Still don't have an answer, though, do we?

We will have an answer, however, if we build an equation...

We know that the 3 numbers add up to 180, so...

x + x + 20 + x + 10 = 180

Group your " x's "...

3x + 20 + 10 = 180

Group the 20 and 10...

3x + 30 = 180

Drop 30 from each side..

3x = 150

x = 50

Still don't have an answer, though, do we?

Almost there - promise...

x = 50

Remember...

1) The smallest = x, so the smallest number is 50.

2) The largest = x + 20, so the largest is 70.

3) The third number = x + 10, so it is 60

50 + 60 + 70 = 180