Final answer:
Emma values the almond half of the cake at $8.00 and the walnut half at $16.00, due to her preference for walnuts. Tommy values both halves equally at $12.00 each because he has no preference between almonds and walnuts.
Step-by-step explanation:
To find the value system of Emma and Tommy for dividing a cake worth $24.00, half almond and half walnut, we must consider their preferences. Emma likes walnuts twice as much as almonds, while Tommy has no preference, liking both equally.
Let's denote the value of the almond half for Emma as x and the value of the walnut half as 2x, knowing that x + 2x equals the total value of the cake, which is $24.00. The equation would be x + 2x = $24.00, which simplifies to 3x = $24.00. Solving for x, we find that x = $8.00. Therefore, the almond half has a value of $8.00 for Emma and the walnut half $16.00 (2x).
For Tommy, who values both halves equally, each half of the cake would have the same value to him. Since the total cost of the cake is $24.00, the value of each half for Tommy is $12.00.