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Pavel [41]
3 years ago
8

Paul has 2/3 as many postcards as Shawn. The number of postcards Shawn has is 4/5 of the number of postcards Tim has. If the thr

ee boys have 280 postcards altogether, how many more postcards does Tim have than Paul?
Mathematics
1 answer:
ahrayia [7]3 years ago
7 0

Tim has 56 more postcards than Paul.

Step-by-step explanation:

Total postcards boys have = 280

Let,

x = Paul's postcards

y = Shawn's postcards

z = Tim's postcards

According to given statement;

x + y + z = 280      Eqn 1

x=\frac{2}{3}y                   Eqn 2

y = \frac{4}{5}z                   Eqn 3

Putting value of y from Eqn 3 in Eqn 2

x=\frac{2}{3}*\frac{4}{5}z\\\\x=\frac{8}{15}z            Eqn 4

Putting value of x and y from Eqn 4 and Eqn 3 in Eqn 1

\frac{8}{15}z+\frac{4}{5}z+z=280\\\\\frac{8z+12z+15z}{15}=280\\\\\frac{35z}{15}=280\\\\

Multiplying both sides by \frac{15}{35}

\frac{15}{35}*\frac{35}{15}z=280*\frac{15}{35}\\z=120

Putting z=120 in Eqn 3

y=\frac{4}{5}*120\\y=96

Putting y=96 in Eqn 2

x=\frac{2}{3}*96\\x=64

Difference of Tim and Paul = 120-64 = 56

Tim has 56 more postcards than Paul.

Keywords: linear equation, substitution method

Learn more about substitution method at:

  • brainly.com/question/10557938
  • brainly.com/question/10600222

#LearnwithBrainly

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