Today Puzzle #790
Puzzle No. 790鈥� Friday 24 July
Mrs Sugar wants to send 50 children a bag of sweets for the holidays. She’s bought a lucky dip of 50 bags which have five different types – chocolates, toffees, fudge, peppermint and liquorice. There’s ½ as many bags of toffee as there are of chocolate, 3 times as many bags of toffee as there are of fudge, 2 more bags of liquorice than there are of peppermints and 1/7 as many bags of peppermints as there are bags of chocolate & fudge combined. How many bags of liquorice are there?
Today’s #PuzzleForToday has been set by Sally Calder, Education Actuary at the Institute and Faculty of Actuaries.
Click here for the answer
Six.
Let the number of bags of peppermints be P. This means the number of bags of liquorice, is P + 2, and the number of bags of chocolate & fudge is P x 7
Let the number of bags of fudge be F. This means that the number of bags of toffee = F x 3 and the number of bags of chocolate = 3 x 2 x F = F x 6
So the number of bags of chocolate & fudge combined is 6F + F = 7F
Which we know is equal to P x 7. Therefore F = P
So the total number of bags is
P (peppermint)
+ (P + 2) (liquorice)
+ 7P (chocolate, and fudge)
+ 3P (toffee)
= 12P + 2 = 50
Therefore P=4, and P + 2 (number of bags of liquorice) = 6
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