Question

Fiona is mixing fertilizer with peat moss to add to her garden. The amount of fertilizer is proportional to the amount of peat moss. Fiona adds 3/4 lb. of fertilizer for every 12 lb. of peat moss. What is the constant of proportionality for the relationship between the weight of the fertilizer and the weight of the peat moss?

A. 1/16
B. 16
C. 3/4
D. 15

Answer 1

The constant of proportionality between the weight of fertilizer and peat moss that Fiona adds to her garden is 1/16, calculated by dividing 3/4 lb. of fertilizer by 12 lb. of peat moss.

Step-by-step explanation:

The constant of proportionality between the weight of the fertilizer and the weight of the peat moss is found by dividing the weight of the fertilizer by the weight of the peat moss. In this case, Fiona adds 3/4 lb. of fertilizer for every 12 lb. of peat moss.

To calculate the constant of proportionality, we set up the ratio:

(Weight of fertilizer) / (Weight of peat moss) = (3/4 lb.) / (12 lb.)

Divide 3/4 by 12 to find the constant:

(3/4) / 12 = 3 / (4×12)

3 / 48 = 1 / 16

The constant of proportionality is 1/16, which means that for every pound of peat moss, 1/16 pound of fertilizer is used. Therefore, the answer is A. 1/16.