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

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.