# Question

The long candles are in multiples of 5, meaning the total number of long candles will end with a 5, or a 0.

Since there are 21 more long candles than short, the total number of short candles will end with a 4, or a 9.

Multiples of 7 which end with a 4 or 9: 14, 49

Since Eva bought less than 50 candles, logically the number of short candles she bought was 14.

14 + 21 = 35

14 ÷ 7 = 2 boxes -> \$5.00

35 ÷ 5 = 7 boxes -> \$22.40

Total spent -> 5 + 22.40 = \$27.40

PS. The answer is either \$27.40 or \$29.50, depending on which price you follow. The text said a box of 5 long candles cost \$3.20, but the diagram stated the cost at \$3.50 per box.

Another way of solving this is simply to guess and check.

But before I start guessing blindly, I would first do a bit of analysing.

The least number of short candles bought is 7.

7 + 21 = 28

So least number of long candles bought would be 30 (smallest number which is multiple of 5, and more than 28)

So I would start my guessing from 30, and stop at 40 since total number of candles is less than 50.

 Long Candles 30 35 40 Short Candles 30 – 21 = 9 35 – 21 = 14 40 – 21 = 19 Is it multiple of 7? No Yes No
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 Short Long Qty per box 7 5 Qty purchased 7u 7u+21

7u+7u+21=14u+21<50 –>14u<29–>u<2.07

So u can only be 1 or 2

 u Short(7u) Long(7u+21) 1 7 28 28 is not multiple of 5 2 14 35 35 is multiple of 5,YES

\$2.5×2+(35/5)*\$3.2=\$27.4

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