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 Question from Jennie, a parent: Paul has 2/3 as many postcards as Shawn. Shawn has 3/5 as many postcards as Tim. If the 3 boys have 280 postcards, how many more postcards does Tim have than Paul?

Hi Jennie,

Sometimes arriving at a solution to a math problem is not as straightforward as the textbooks make it look. You may have to try different approaches until you find one that works. Suppose for this problem you let $P$ be the number of postcards that Paul has, $S$ be the number of postcards that Shawn has and $T$ be the number of postcards that Tim has. Then you know that

$P + S + T = 280.$

If you can express $P, S$ and $T$ all in terms of the same variable you can solve for it and as a result solve the problem.

First approach:

Try to express $P, S$ and $T$ in terms of $P.$ You are told that "Paul has 2/3 as many postcards as Shawn" so that is $P = \frac23 S.$ This expresses $P$ in terms of $S$ rather than $S$ in terms of $P$ so let's try another approach.

Second approach:

Try to express $P, S$ and $T$ in terms of $S.$ You are told that "Paul has 2/3 as many postcards as Shawn" so that is $P = \frac23 S.$ You are also told that "Shawn has 3/5 as many postcards as Tim" which is $S = \frac35 T.$ This expresses $S$ in terms of $T$ so lets try a third approach.

Third approach:

Try to express $P, S$ and $T$ in terms of $T.$ You are told that "Shawn has 3/5 as many postcards as Tim." which is $S = \frac35 T.$ Now the what does the fact that "Paul has 2/3 as many postcards as Shawn" tell you? Substitute into the expression $P + S + T = 280$ and solve for $T.$

Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.