Questions: 28. Three chocolate bars of 12,24 , and 30 grams are broken apart so that all of the pieces of all 3 bars are of equal weight. What is the fewest total number of chocolate bar pieces? A) 11 B) 13 C) 15 D) 17

Solution Steps

We have three chocolate bars weighing 12 grams, 24 grams, and 30 grams. These bars are broken into smaller pieces such that all the pieces from all three bars are of equal weight. The goal is to find the fewest total number of pieces.

To ensure all pieces are of equal weight, the weight of each piece must be a common divisor of 12, 24, and 30. The largest possible weight for each piece is the greatest common divisor (GCD) of these numbers.

• The GCD of 12, 24, and 30 is 6.

Now, divide each chocolate bar by the GCD to find the number of pieces for each bar:

• For the 12-gram bar: \( \frac{12}{6} = 2 \) pieces.
• For the 24-gram bar: \( \frac{24}{6} = 4 \) pieces.
• For the 30-gram bar: \( \frac{30}{6} = 5 \) pieces.

Add up the number of pieces from each bar to get the total number of pieces:

\[ 2 + 4 + 5 = 11 \]

Final Answer