Paul has 2/3 as many postcards as Shawn . The number of postcards Shawn has is 3/5 of the number of postcards Tim has. If the three boys have 280 postcards altogether,how many more postcards does Tim have than Paul ?
Let's use algebra to solve the problem.
Let's say that the number of postcards that Shawn has is "x". Then, we know that Paul has 2/3 as many postcards as Shawn, so Paul has (2/3)x postcards.
We also know that the number of postcards Shawn has is 3/5 of the number of postcards Tim has. Let's call the number of postcards that Tim has "y". Then, we can write an equation:
x = (3/5)y
Finally, we know that the three boys have 280 postcards altogether, so we can write another equation:
x + (2/3)x + y = 280
We can simplify the first equation by multiplying both sides by 5/3:
(5/3)x = y
Substituting this into the second equation gives:
x + (2/3)x + (5/3)x = 280
Multiplying through by 3 gives:
3x + 2x + 5x = 840
Simplifying, we get:
10x = 840
x = 84
So Shawn has 84 postcards, Paul has (2/3)84 = 56 postcards, and Tim has (5/3)84 = 140 postcards.
Therefore, Tim has 140 - 56 = 84 more postcards than Paul.
Answer: Tim has 84 more postcards than Paul.
I would have defined y as the number of cards that Tim has, since he is the last referenced.
then Shawn has (3/5)y , and
Paul has (2/3)(3/5)y or 2/5 y
y + 3/5 y + 2/5 y = 280
2y = 280
y = 140
So Tim has 140
Shawn has 3/5 of 140 = 84
and Paul has 2/3 of 84 or 56
Tim's number - Paul's number = 140 - 56 = 84