Question

Determine if the quantities in the data table are in a proportional relationship, if they are not in a proportional relation indicate why?
#of trees #of apples
2. 26
3. 39
6. 78
10. 130
12. 156

A.-yes the data table has a proportional relationship
B-No the ratios are not equivalent
C-no the ratio 6:78 is not proportional to the other ratios
D-no the table does not count consecutively

Answer 1

To determine if the quantities in the data table are in a proportional relationship, we can check if the ratios of the two quantities are equivalent.

The given data is:

- For 2 trees, there are 26 apples: \( \frac{26}{2} = 13 \)
- For 3 trees, there are 39 apples: \( \frac{39}{3} = 13 \)
- For 6 trees, there are 78 apples: \( \frac{78}{6} = 13 \)
- For 10 trees, there are 130 apples: \( \frac{130}{10} = 13 \)
- For 12 trees, there are 156 apples: \( \frac{156}{12} = 13 \)

Since all these ratios simplify to \( 13 \), they are equivalent.

Therefore, the answer is:

A.- yes the data table has a proportional relationship.