Karen and Kate lookedata collection of stones. Karen said the ratio 2:3 represented the stones. Kate said the ratio 2:5 represented the stones. They were both right. Explain Why
It would help if you told us what the ratio represents. Perhaps there are two types of stone, and 2:3 is the ratio of the numbers of one to the other (A to B) and the other is the ratio of A to the total (A+B)
thank you drwls. that is all the problem provides. is this a bad question?
2x+3y=6
To explain why both Karen and Kate were right, first, let's understand what a ratio represents. A ratio is a way of comparing two or more quantities. It shows how many times one quantity is contained in another. Ratios are typically expressed in the form of a:b, where a and b are numbers representing the quantities being compared.
In this case, Karen said the ratio 2:3 represented the stones, while Kate said the ratio 2:5 represented the stones. We need to find a situation where both ratios can be correct.
One way to find a situation where both ratios are correct is to find a common multiple of the two denominators (the numbers after the colon). In this case, the denominators are 3 and 5.
The least common multiple (LCM) of 3 and 5 is 15. So, we can assume that there are 15 stones in total.
To find how many stones are represented by each ratio, we need to divide the total number of stones by the sum of the parts in each ratio.
For Karen's ratio 2:3, the sum of the parts is 2 + 3 = 5.
So, Karen's ratio represents (2/5) * 15 = 6 stones.
For Kate's ratio 2:5, the sum of the parts is 2 + 5 = 7.
So, Kate's ratio represents (2/7) * 15 = about 4.29 stones.
When rounded to the nearest whole number, Karen's ratio represents 6 stones, and Kate's ratio represents 4 stones.
So, Karen was right that the ratio 2:3 represented 6 stones, and Kate was also right that the ratio 2:5 represented 4 stones, as 6 and 4 are included in the total of 15 stones.