Upper Elementary:
Question: Barb's birthday cake has 1 more candle than the number of years she has been alive. If 1/2 of the candles are blue, 1/3 of the candles are green, and the remaining 4 candles are yellow, then how old is Barb?
Answer: 23 years old
Solution: In order to compare the fractional parts, we need to give them the same denominator – in this case, 2 × 3 = 6. 1/2 × 3/3 = 3/6 of the candles are blue, and 1/3 × 2/2 = 2/6 of the candles are green. This means that 3/6 + 2/6 = 5/6 of the candles are blue or green, leaving 1 – 5/6 = 1/6 of the candles yellow. If 1/6 of the candles is the same as 4 candles, then the whole number of candles must be 6 x 4 = 24. If there is 1 more candle on the cake than the number of years Barb has been alive, then she is 24 - 1 = 23 years old.
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