Elizabeth is an event planner who has been hired to plan a class reunion. The class has 275 people and 256 people will be attending. Elizabeth must plan the seating decorations and food.
The school colors are blue and white. Elizabeth has 84 blue balloons and w white balloons. If the greatest amount of balloon bouquets she can make is 12, what are all of the possible values of w?
all multiples of 12
To find the possible values of w, we need to consider the given information and set up an equation.
Given:
- Total number of people in the class: 275
- Number of people attending the reunion: 256
- Number of blue balloons available: 84
- Number of white balloons: w
- Maximum number of balloon bouquets she can make: 12
Let's denote the number of blue balloons used in each bouquet as b and the number of white balloons used as w.
Each bouquet will consist of a combination of blue and white balloons. The total number of balloons in each bouquet is given by the sum of blue and white balloons used:
b + w
We are also given that the maximum number of bouquet arrangements is 12. So, we can write the equation:
b + w ≤ 12
Since we have 84 blue balloons, we can calculate the maximum number of bouquets using all blue balloons:
84 / b
Similarly, the maximum number of bouquets using all white balloons would be:
w / w
To find the possible values of w, we need to satisfy the conditions:
1. The total number of balloons used in each bouquet is less than or equal to 12.
2. The maximum number of bouquets using all blue balloons (84) should be less than or equal to 12.
3. The maximum number of bouquets using all white balloons (w) should be less than or equal to 12.
Let's evaluate these conditions:
1. b + w ≤ 12
2. 84 / b ≤ 12
3. w / w ≤ 12
To find the possible values of w, we need to find the solution to these conditions.