How much fruit in each basket?

Question

Anna has 15 apples, 9 oranges, and 18 mangoes. She wants to put all of the fruit into decorative baskets. Each basket must have the same number of pieces of fruit in it. Without mixing fruits, what is the greatest number of pieces of fruit that Anna can put in each basket?

Answer 1

Anna has 15 apples, 9 oranges, and 18 mangoes. She wants to put all of the fruit into decorative baskets. Each basket must have the same number of pieces of fruit in it. Without mixing fruits, what is the greatest number of pieces of fruit that Anna can put in each basket?

First, let's analyze the problem (that is, take it apart and reword it).

"put all of the fruit into decorative baskets" means that 15+9+18=42 pieces of fruit must be put into baskets. So, if Anna wanted to put one piece of fruit into each basket, she would have 42 baskets that satisfy, "Each basket must have the same number of pieces of fruit in it." However, that does not satisfy, "what is the greatest number of pieces of fruit that Anna can put in each basket."

Let's see how each fruit can be distributed.

What number(s) divide evenly into 15, 9, and 18 (that is called a "common divisor"? And, what is the largest number that divides into them all; it is the "maximum common divisor" (MCD). We would like the MCD because we want to satisfy "what is the greatest number of pieces of fruit that Anna can put in each basket?"

We want a divisor that leaves no remainder. To factor each number as much as possible, we will find "the prime factors." That is because a composite factor may be further broken down into prime factors.

The factors of:

15 = 3 * 5

9 = 3 * 3

18 = 2 * 3 * 3

The most common numbers in all of these is "3". (the MCD)

Anna may use 3 decorative baskets. They each contain: 5 apples (15/3), 3 oranges (9/3), and 6 mangoes (18/3). Notice that"

1. that is all of the fruit;
2. Each basket must have the same number of pieces of fruit in it. There are 14 pieces of fruit in each basket.
3. This is the greatest number of fruit that Anna can put into each basket (because 3 is the largest value that will divide into all of 15, 9, and 18).

The greatest number of pieces of fruit that Anna can put into each basket is 14 (that is, 5+3+6). And, 14*3=42.