Tim has 84 more postcards than Paul.
Step-by-step explanation:
Given,
Total number of postcards = 280
Let,
Tim's share of postcards = x
Shawn's share of postcards = [tex]\frac{3}{5}\ of\ Tim's\ share[/tex] = [tex]\frac{3}{5}x[/tex]
Paul's share of postcards = [tex]\frac{2}{3}\ of\ Shawn's=\frac{2}{3}(\frac{3}{5}x)=\frac{2}{5}x[/tex]
According to given statement;
[tex]x+\frac{3}{5}x+\frac{2}{5}x=280[/tex]
Taking LCM
[tex]\frac{5x+3x+2x}{5}=280\\\\\frac{10x}{5}=280\\\\2x=280[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{280}{2}\\x=140[/tex]
Paul's share = [tex]\frac{2}{5}x=\frac{2}{5}(28)=56[/tex]
Difference = Tim's share - Paul's share
Difference = 140 - 56 = 84 cards
Tim has 84 more postcards than Paul.
Keywords: addition, fraction
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