Word Problem with Averages in 3rd & 4th Grade Maths

Math Word Problem with Averages: 12 marbles were given to Tom, Amy & Sue. Tom has 2 marbles less than the average, while Sue has 4 more marbles than Amy. How many marbles does each of them have?

Solving: Let’s start by jotting down the clues in a logical manner:

1. Total number of marbles = 12
2. Total number of kids = 3
3. Average marbles per kid = 12/3 = 4
4. Some kids will have more marbles than the average, some kids may have less marbles than the average while some kids may have the same number of marbles as the average
5. Tom has 2 marbles less than average
6. Sue has 4 marbles more than Amy

So from (5), Tom has 2 marbles less than 4. 

So Tom must have (4-2) = 2 marbles ———- (let us mark this as 7)

So, Amy + Sue will have the rest of the marbles.

So, Amy + Sue will have (12 marbles – 2 marbles that Tom has) = 10 marbles

So Amy + Sue has 10 marbles ———- (let us mark this as 8)

From clue (6), if Amy has X number of marbles, then Sue will have (x+4) marbles ———- (let us mark this as 9)

Since Amy + Sue has 10 (from point 8 above),

=> X + (X+4) = 10 

=> 2X + 4 = 10

=> 2X = 10 – 4

=> 2X = 6

=> X = 6/2 (dividing both sides by 2)

=> X = 3

Since X is the number of marbles that Amy has, we can now say that Amy has 3 marbles.

If we put this back in equation (9):

Sue will have X + 4 marbles, => Sue has (3+4) marbles

So Sue has 7 marbles.

Answer: Tom has 2 marbles, Amy has 3 marbles & Sue has 7 marbles.