Ninety-two sweets between three children. Ana gets three times what Ben gets, Cal gets two more than Ben. Three unknowns, one number — and it is enough.
It looks like too little information, and the way out is to stop treating the three shares as three separate mysteries. Both of the others are described in terms of Ben's share, so call Ben's share one part: Ana has three parts, Cal has one part and two more. The whole total is five parts plus two. Take the two off the top and what is left divides cleanly.
Why this sheet works
The wrong first move is the one every earlier sharing question rewarded: divide by three. Here it is wrong twice — the shares are not equal, and the totals on these sheets do not even divide by three, so the mistake fails visibly instead of landing somewhere plausible.
Find the smallest share. Show how you worked it out.
1Ben, Ana and Cal share 119 sweets. Ana gets 2 times as many as Ben, and Cal gets 3 more than Ben.How many does Ben get?Why
2112 books go onto three shelves. The middle shelf holds 2 times what the top shelf holds, and the bottom shelf holds 8 more than the top.How many books are on the top shelf?Why
Sharing puzzlesTotals to 120
Name: Date:
Find the smallest share. Show how you worked it out.
3Three teams pick 118 apples between them. Blue picks 2 times as many as Red, and Green picks 2 more than Red.How many does Red pick?Why
4A prize of 109 tokens is split between Iris, Jon and Kit. Jon takes 2 times Iris's share, and Kit takes 9 more than Iris.How many tokens does Iris get?Why
Sharing puzzles · Totals to 120Answer key
1. Call Ben's share one part. Then Ana has 2 parts, and Cal has one part and 3 more. That is 4 parts and 3 extra, adding to 119. Take the 3 off first: 119 − 3 = 116. Now 116 ÷ 4 = 29, so one part is 29 sweets.2. Call the top shelf's share one part. Then the middle shelf has 2 parts, and the bottom shelf has one part and 8 more. That is 4 parts and 8 extra, adding to 112. Take the 8 off first: 112 − 8 = 104. Now 104 ÷ 4 = 26, so one part is 26 books.3. Call Red's share one part. Then Blue has 2 parts, and Green has one part and 2 more. That is 4 parts and 2 extra, adding to 118. Take the 2 off first: 118 − 2 = 116. Now 116 ÷ 4 = 29, so one part is 29 apples.4. Call Iris's share one part. Then Jon has 2 parts, and Kit has one part and 9 more. That is 4 parts and 9 extra, adding to 109. Take the 9 off first: 109 − 9 = 100. Now 100 ÷ 4 = 25, so one part is 25 tokens.
