Final answer:
The student can make 3 complete bouquets of balloons, with each bouquet having 6 balloons of each color, using the 18 yellow, 30 blue, and 42 red balloons.
Step-by-step explanation:
To determine the number of bouquets that can be made with 18 yellow, 30 blue, and 42 red balloons, where each bouquet has the same number of each color, we need to find the greatest common divisor (GCD) of the three numbers. The GCD of 18, 30, and 42 is the largest number that divides all of them without leaving a remainder.
Step by step, we find the GCD like this:
- Factors of 18 are 1, 2, 3, 6, 9, 18.
- Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30.
- Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42.
The common factors of 18, 30, and 42 are 1, 2, 3, and 6. The greatest of these is 6. So, the GCD is 6.
Therefore, each bouquet can contain 6 balloons of each color. To find out how many bouquets can be made, we divide the number of each color of balloons by 6:
- 18 yellow balloons ÷ 6 = 3 bouquets of yellow balloons.
- 30 blue balloons ÷ 6 = 5 bouquets of blue balloons.
- 42 red balloons ÷ 6 = 7 bouquets of red balloons.
Thus, the maximum number of bouquets that can be made, with each bouquet having the same number of each color, is 3, which is the number of complete bouquets we can make from the color with the smallest number available (yellow).
The student can make 3 complete bouquets of balloons using 18 yellow, 30 blue, and 42 red balloons.