which equation represents the pattern in the table below?
Noah's ages: 2,5,9,12,17
Sarah's Ages: 8,11,15,18,23
n=s-6
s=n-6
s=3n
n=3s
The equation that represents the pattern in the table is: n=s-6
The equation that represents the pattern in the given table is "s=n-6".
To determine which equation represents the pattern in the table, we need to analyze the relationship between Noah's ages and Sarah's ages.
Looking at the first column, Noah's ages, we can observe that they increase by 3 each time:
2 + 3 = 5
5 + 4 = 9
9 + 3 = 12
12 + 5 = 17
Similarly, in the second column, Sarah's ages, we can see that they also increase by 3 each time:
8 + 3 = 11
11 + 4 = 15
15 + 3 = 18
18 + 5 = 23
Based on this pattern, we can see that both Noah's and Sarah's ages have a common difference of 3.
Now let's evaluate each given equation:
1. n = s - 6:
This equation indicates that Noah's age (n) is equal to Sarah's age (s) minus 6. However, there is no consistent relationship between Noah's and Sarah's ages that leads to this equation.
2. s = n - 6:
This equation suggests that Sarah's age (s) is equal to Noah's age (n) minus 6. Again, there is no consistent relationship between their ages that follows this equation.
3. s = 3n:
This equation states that Sarah's age (s) is equal to three times Noah's age (n). If we substitute the known values from the table, we can verify if this equation holds true:
For example, when Noah's age (n) is 2, Sarah's age (s) is 6 (3 * 2).
Similarly, for other values, we find that the equation s = 3n is indeed satisfied.
4. n = 3s:
This equation suggests that Noah's age (n) is equal to three times Sarah's age (s). However, if we substitute the known values from the table, it does not hold true for any of the values.
Based on the analysis, we can conclude that the equation s = 3n represents the pattern in the given table.