The school colors are blue and white. Elizabeth has 84 blue balloons and 96 white balloons. How many balloon bouquets can she make if she wants to haVe the same number of each color in each bouquet and use all balloons?
What is the greatest common factor of 84 and 96?
12
To find out how many balloon bouquets Elizabeth can make, we need to determine the maximum number of balloons she can put in each bouquet while ensuring equal numbers of blue and white balloons.
First, let's determine the common number of balloons in each bouquet. This number should be a divisor of both 84 and 96. To find the greatest common divisor (GCD) of 84 and 96, we can use the Euclidean algorithm.
Divide 96 by 84:
96 ÷ 84 = 1 remainder 12
Now divide 84 by the remainder (12):
84 ÷ 12 = 7 remainder 0
Since the remainder is 0, 12 is the GCD of 84 and 96.
This means that Elizabeth can put 12 balloons of each color in each bouquet.
Now, let's find the number of bouquets she can make by dividing the total number of balloons by the number of balloons per bouquet.
The total number of balloons Elizabeth has is 84 (blue) + 96 (white) = 180 balloons.
Divide 180 by 12:
180 ÷ 12 = 15
Therefore, Elizabeth can make 15 balloon bouquets if she wants to have the same number of each color in each bouquet and use all the balloons.