the average of 4 three digit numbers is 250. two of the numbers are 190 and 230. What is the largest difference between the other 2 numbers?

Question

It is a word problem which involves thinking.

Answer 1

We know that the average is the sum of the terms divided by the number of terms.  We are given 2 three digit numbers.

 

Assign variables for the other 2 three digit numbers.

 

Let one of the 2 three digit numbers = x

Let the other three digit number = y

 

Write an equation that represents the average.

 

(x + y + 190 + 230) / 4 = 250

 

 

Simplify this equation.

 

(x + y + 420) / 4 = 250

 

x + y + 420 = 1000

 

x + y = 580       

 

 

We know that x and y both have 3 digits.  Their sum is 580 according to the equation.

 

Lets pick 100 as one and 480 as the other.   We pick 100 because its the lowest three digit number in the number system. If we include these number  into the average, will the average be 250?  Lets see.

 

(100 + 480 + 190 + 230) / 4 = 250

 

1000 / 4 = 250

 

250 = 250

 

This works.

 

 

What if we chose 101 and 479?  Will this work?

 

(101 + 479 + 190 + 230) / 4 = 250

 

1000 / 4 = 250

 

250 = 250

 

Yes it does.

 

 

Compare the differences between the two pairs.

 

480 - 100 = 380

 

479 - 101 = 378

 

 

If we follow a pattern,

 

478 - 102 = 376

 

477 - 103 = 374

 

476 - 104 = 372

 

475 - 105 = 370

 

 

The difference only decreases.  So the largest difference between the 2 numbers that make the average 250 is 380.