Ann is grouping 38 rocks. She can put them into groups of 10 rocks or as single rocks.what are different ways Ann can group the rocks?
The correct answer and explanation is:
Okay, let’s figure out the different ways Ann can group her 38 rocks using only groups of 10 or single rocks.
The correct answer is:
There are four different ways Ann can group the 38 rocks:
- 3 groups of 10 rocks and 8 single rocks.
- 2 groups of 10 rocks and 18 single rocks.
- 1 group of 10 rocks and 28 single rocks.
- 0 groups of 10 rocks and 38 single rocks.
Explanation:
Ann has a total of 38 rocks and she can arrange them in two types of groups: groups of exactly 10 rocks, or as individual single rocks. We need to find all the combinations of these two types of groupings that add up to a total of 38 rocks.
We can think about this by considering the maximum number of groups of 10 Ann could possibly make. Each group of 10 uses up 10 rocks.
- If Ann made 1 group of 10, she would use 10 rocks (1 * 10 = 10). She would have 38 – 10 = 28 rocks left, which she would have to keep as single rocks. So, one way is 1 group of 10 and 28 single rocks.
- If Ann made 2 groups of 10, she would use 20 rocks (2 * 10 = 20). She would have 38 – 20 = 18 rocks left, which must be single rocks. Another way is 2 groups of 10 and 18 single rocks.
- If Ann made 3 groups of 10, she would use 30 rocks (3 * 10 = 30). She would have 38 – 30 = 8 rocks left, which would be single rocks. This gives us a third way: 3 groups of 10 and 8 single rocks.
- Can Ann make 4 groups of 10? 4 groups of 10 would be 40 rocks (4 * 10 = 40). Ann only has 38 rocks, so she doesn’t have enough to make 4 full groups of 10. Therefore, the maximum number of groups of 10 she can make is 3.
We also need to consider the possibility that Ann makes no groups of 10.
- If Ann makes 0 groups of 10, she uses 0 rocks in groups of