A florist has 48 roses, 32 tulips, and 16 carnations she must use to create bouquets. Each bouquet must have an equal number of each type of flower as the other bouquets. What is the largest number of bouquets she can make without having any flowers left over?
No, she can make 16 bouquets, each with 3 roses, 2 tulips, and 1 carnation
To have an equal number of each type of flower in each bouquet, the number of roses, tulips, and carnations must all be divisible by the same number.
The greatest common divisor of 48, 32, and 16 is 16, since 16 divides evenly into all three numbers.
Dividing 48 by 16, we get 48/16 = <<48/16=3>>3 bouquets worth of roses.
Dividing 32 by 16, we get 32/16 = <<32/16=2>>2 bouquets worth of tulips.
Dividing 16 by 16, we get 16/16 = <<16/16=1>>1 bouquet worth of carnations.
Therefore, the florist can make a maximum of <<3+2+1=6>>6 bouquets without any flowers left over. Answer: \boxed{6}.
Apologies for the mistake. You are correct.
To find the maximum number of bouquets, we need to find the largest possible number that divides evenly into 48, 32, and 16.
The greatest common divisor of 48, 32, and 16 is 16, since 16 divides evenly into all three numbers.
Dividing 48 by 16 gives 48/16 = 3 bouquets worth of roses.
Dividing 32 by 16 gives 32/16 = 2 bouquets worth of tulips.
Dividing 16 by 16 gives 16/16 = 1 bouquet worth of carnations.
Therefore, the florist can make a maximum of 3 bouquets of roses, 2 bouquets of tulips, and 1 bouquet of carnations, for a total of 3 + 2 + 1 = 6 bouquets. Since each bouquet will have an equal number of each type of flower (3 roses, 2 tulips, and 1 carnation), we can make 6 bouquets without any flowers left over.
So, the largest number of bouquets the florist can make without having any flowers left over is 6.