Three teachers were discussing how long they had been teaching.
Alex and Billie had been teaching for a total of 36 years. Charlie and Billie had been teaching for a total of 22 years. Charlie and Alex had been teaching for a total of 28 years.
How long had each been teaching?
Hint
If we look at all of the clues, each person appears exactly twice.
Answer
Alex had been teaching for 21 years.
Billie had been teaching for 15 years.
Charlie had been teaching for 7 years.
Reasoning
If we look at all of the clues, each person appears exactly twice.
So the total of the three clues gives us two lots of Alex + Billie + Charlie = 36 + 22 + 28 = 86.
So, Alex + Billie + Charlie = 43 years.
In each clue we are given two of the people, so we can use this to find the missing person:
Charlie and Billie had been teaching for a total of 22 years, which means that Alex must be: 43 − 22 = 21 years.
Charlie and Alex had been teaching for a total of 28 years, which means that Billie must be: 43 − 28 = 15 years.
Alex and Billie had been teaching for a total of 36 years, which means that Charlie must be: 43 − 36 = 7 years.
Reasoning With Algebra
Let Alex = A, Billie = B and Charlie = C, then:
[1] A + B = 36 [2] C + B = 22 [3] C + A = 28
If we use [3] − [2] we have:
[4] A − B = 6
If we use [1] + [4] we have:
2A = 42 A = 21
By [1] B = 15. By [3] C = 7.
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Puzzle 198
In each of these sentences, can you replace the missing number.
The number is written as a word (e.g. five, twenty-four, thirty-three), and each sentence is correct after the replacement.
This sentence contains ? X. Slightly trickier, this sentence contains ? R's. Even trickier, this sentence contains precisely ? E's. This sentence has exactly ? letters. This sentence, hopefully, contains ? letters, one hyphen, five commas, and four Y's. To finish, if this sentence had a T removed, it would contain ? letters!
Hint
Start by counting the letters you're already given.
Answers This sentence contains one X.Slightly trickier, this sentence contains four R's.Even trickier, this sentence contains precisely ten E's.This sentence has exactly thirty-nine letters.This sentence, hopefully, contains seventy-five letters, one hyphen, five commas, and four Y's.To finish, if this sentence had a T removed, it would contain sixty-two letters!
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Puzzle 199
Using all of the letters A to Z, each once only, complete these common words. ba-g-d--eddia---uo-ai-de--o-el-um-spy--yg-ou---naltra---umb-d--ty
