A cake entrepreneur bought 3 sacks of flour, 2 sacks of coconuts, and 6 dozen eggs. After the cake was made, it turned out that there were still 6 eggs left. Suppose x, y, and z are the prices of a sack of flour, a sack of coconuts, and half a dozen eggs (in rupiah), respectively. The algebraic form of the price of the cake ingredients used is ... rupiah. A. 3x+2y+12z B. 3x+2y+11z C. 3x+2y+6z D. 3x+2y+5.5z

1 answer

To determine the algebraic form of the price of the cake ingredients used, we will consider each ingredient separately and account for the quantities purchased.

  1. Flour: The entrepreneur bought 3 sacks of flour. If the price of a sack of flour is \(x\), then the total cost for the flour is: \[ 3x \]

  2. Coconuts: The entrepreneur bought 2 sacks of coconuts. If the price of a sack of coconuts is \(y\), then the total cost for the coconuts is: \[ 2y \]

  3. Eggs: The entrepreneur bought 6 dozen eggs. Since there are 12 eggs in a dozen, 6 dozen equals \(6 \times 12 = 72\) eggs. The problem states that there are 6 eggs left after making the cake, so the number of eggs used is: \[ 72 - 6 = 66 \text{ eggs} \] If the price of half a dozen eggs is \(z\), then the price of one dozen eggs would be \(2z\). Therefore, the cost of 66 eggs is: \[ 66 \text{ eggs} \times \left(\frac{z}{6 \text{ eggs}}\right) = 66 \times \frac{2z}{12} = 11z \]

Now, combining all these costs together, the total cost of the ingredients used can be expressed as: \[ 3x + 2y + 11z \]

Thus, the algebraic form of the price of the cake ingredients used is: \[ \boxed{3x + 2y + 11z} \]

The correct answer is B. 3x + 2y + 11z.