Pow 3 "a sticky gum" revisited
Gumballs are 1 penny each. The kids each want a different color. what is the maximum spent with each generalization. create formulas for the following.
Generalize the number of children. Generalize the number of gum ball each child wants. Generalize the number of gum balls of each color. Generalize the number of colors in the machine.
To find the maximum amount spent for each generalization, let's break down the problem step by step and create formulas for each scenario.
1. Generalize the number of children:
Let's assume the number of children is represented by the variable 'n'. Each child wants a different color, so the total amount spent is equal to the number of children multiplied by the price of a gumball. Thus, the formula would be: Amount spent = n * 1 penny.
2. Generalize the number of gumballs each child wants:
Suppose the number of gumballs each child wants is represented by the variable 'g'. In this case, the total amount spent is equal to the number of children multiplied by the number of gumballs each child wants, and then multiplied by the price of a gumball. The formula would be: Amount spent = n * g * 1 penny.
3. Generalize the number of gumballs of each color:
Assuming the number of gumballs of each color is represented by the variable 'm', and there are 'c' different colors in the machine. In this scenario, the total amount spent is calculated by multiplying the number of children, the number of gumballs each child wants, the number of gumballs of each color, and then the price of a gumball. The formula would be: Amount spent = n * g * m * c * 1 penny.
4. Generalize the number of colors in the machine:
If the number of colors in the machine is represented by the variable 'k', we again have the number of children, the number of gumballs each child wants, the number of gumballs of each color, the number of colors in the machine, and the price of a gumball. The formula would be: Amount spent = n * g * m * k * 1 penny.
Remember to convert the final answer from pennies to the desired currency if needed.
By generalizing each of these variables, you can easily calculate the maximum amount spent for different scenarios of the gumball machine.