In a shop, candles are sold only in boxes. A box of 7 short candles costs $2.50 and a box of 5 long candles costs $3.20.

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(a) Dan wants 19 short candles and 3 long candles for his lanterns. What is the least amount of money that Dan will need to spend on the candles?

(b) Eva bought 21 more long candles than short candles from the shop. The total number of candles she bought was fewer than 50. How much did Eva spend on the candles altogether?

Since (a) is rather straightforward, we will skip straight to (b) in this discussion.

The model answer given in the book uses the guess-and-check method. In that answer, the number that is first checked is the total number of long candles. That number is 25 (since 25 is a multiple of 5, and 21 less than 25 does not yield a negative number).

While there’s nothing wrong to start by checking the number of long candles, it’s more direct to work from the number of short candles instead. Watch the video solution below.

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