3 out of 4 - Again. What if there is no 3rd number?

Here's a quick review...



"A 10 metre flag pole casts a shadow of 6 metres. A 12 metre pole would cast a shadow that is ______ metres in length."

"A motorcyclist rides 125 miles in 3 hours. At this rate, how much distance will be covered in 5 hours?"

A factory produces 3000 widgets every 45 minutes. How many widgets will be produced in 7 hours?


These questions, I like to call, are "3 out of 4" questions. You are given 3 numbers and you need to find the 4th. How to solve? Make yourself a 4-way relationship box. 


Let's look at question 1 again. 

"A 10 metre flag pole casts a shadow of 6 metres. A 12 metre pole would cast a shadow that is ______ metres in length."

Your two "measurements" are height (H) and shadow length (SL).

H           SL
10            6
12            ?

Remember MUADO - Multiply Up and Across, Divide by the Other Number.

12 x 6 = 72
72/10 = 7.2

You could have set your box up another way.

H      10    12
SL     6      ?

6 x 12 = 72
72/10 = 7.2

Same answer...


Tricks to watch out for!

In question 3, the two "measurements" are time and widgets. However, the first "time" is in minutes and the second one is in hours. You need to either convert the 45 minutes to .75 hours, or convert the 7 hours to 420 minutes. Then set up your box, remember MUADO, and get yourself the right answer.

So...

What if the question has no 3rd number? 

For example...

You need to answer 40 questions correctly on an exam in order to get the 80% passing mark. How many questions are on the exam?

Where's the 3rd number?

The third number is 100 - the % means 100.

Your two "measurements" are questions answered correctly (Q) and percent (%).

Q           %
40           80
?            100


Another example...

Pat can cut a lawn in 45 minutes? How long will it take Pat to cut 2.5 lawns?

Where's the 3rd number?

The third number is 1 - "a lawn" = 1.

Your two "measurements" are lawns (L) and time (T).

L           T
1           45
2.5         ?