The range of the cards is 6, the median of the cards is 7, the mean of the cards is 8, work out the missing numbers

Question:

There are 5 cards in order from smallest to largest, 5 _ _ _ _. The range of the cards is 6, the median of the cards is 7, the mean of the cards is 8, work out the missing numbers

5, 6, 7, 11, 11 or 5, 7, 7, 10, 11

Step-by-step explanation:

Given

Required

Complete the blanks

Range is calculated as:

From the given numbers, we have:

So, the equation becomes

So, we have:

5 _ _ _ 11

Next,

means that the middle number is 7;

So, we have:

5 _ 7 _ 11

Next,

Let the two remaining blanks be x and y: 5 x 7 y 11

Where

and

So, we have:

Collect like terms

Cross Multiply

Recall that: and

Using trial by error, we have:

Hence, the complete cards could be: 5, 6, 7, 11, 11 or 5, 7, 7, 10, 11