Sample Problem

Gary has half as many stamps as Frank. Rex has 38 more stamps than Gary. The average number of stamps each of them has is 214. How many stamps does Frank have?

stamps

Solution

Since each boy has an average of 214 stamps, they have 214 × 3 = 642 stamps altogether.

Since Gary has half as many stamps as Frank, Frank’s stamps = Gary’s stamps × 2.

Since Rex has 38 more stamps than Gary, Rex’s stamps = Gary’s stamps + 38.

We can solve this problem using trial and error. Pick a number for Gary’s stamps, plug in for Frank’s stamps and Rex’s stamps, and add the three numbers together to see if the sum equals 642. If your first number doesn’t work, pick a smaller number if the sum is too big and a bigger number if the sum is too small. Keep doing this until you get 642 as your sum.

 Number of Gary’s Stamps Number of Frank’s stamps Number of Rex’s stamps Sum 100 100 × 2 = 200 100 + 38 = 138 100 + 200 + 138 = 438 150 150 × 2 = 300 150 + 38 = 188 150 + 300 + 188 = 638 155 155 × 2 = 310 155 + 38 = 193 155 + 310 + 193 = 658 152 152 × 2 = 304 152 + 38 = 190 152 + 304 + 190 = 646 151 151 × 2 = 302 151 + 38 = 189 151 + 302 + 189 = 642

Frank has 302 stamps.