Question

a vegetarian ate 4.35 kg of carrots to get full. on another day he required 3.51 kg of broccoli to get full. assume his stomach was equally full on the two occasions. show that the conversion factor between carrots and broccoli is equal to 1 by writing the equality, then dividing both sides by carrots. 1 stomach = 1 kg carrots = 2 kg broccoli. also, 2 stomach = 3 kg carrots = 4 kg broccoli. the relationship is a direct proportion and we can use it as a conversion factor. how many kg carrots are there in 155.5 kg broccoli? 5 (6)(--------) = 7 8 a. 3.51 b. 7.02 c. 4.35 d. 8.70 e. 193 f. 4.35 kg carrots g. 155.5 kg broccoli h. 193 kg carrots i. 3.51 kg broccoli

Explanation:

Step1: Identify the conversion - ratio

We know that when the stomach is full, 4.35 kg of carrots = 3.51 kg of broccoli. The conversion factor from broccoli to carrots is $\frac{4.35}{3.51}$.

Step2: Calculate the amount of carrots for 155.5 kg of broccoli

Let $x$ be the amount of carrots for 155.5 kg of broccoli. We set up a proportion: $\frac{x}{155.5}=\frac{4.35}{3.51}$. Then $x = 155.5\times\frac{4.35}{3.51}$.
$x=\frac{155.5\times4.35}{3.51}=\frac{676.425}{3.51}=193$.

Answer:

H. 193 kg carrots