Question

1. in 200 grams of beef soup, there are 80 micrograms of vitamin a. let x represent the amount of grams of beef soup and y represent the micrograms of vitamin a in the beef soup. which equations represent the relationship between grams of soup and vitamin a? select all that apply.

a. ( y = \frac{2}{5}x )
b. ( y = \frac{5}{2}x )
c. ( x = \frac{2}{5}y )
d. ( x = \frac{5}{2}y )

Explanation:

Step1: Find the ratio

We know that in 200 grams of soup (\(x = 200\)), there are 80 micrograms of Vitamin A (\(y = 80\)). The ratio of \(y\) to \(x\) is \(\frac{y}{x}=\frac{80}{200}=\frac{2}{5}\), so \(y=\frac{2}{5}x\) (checking option A). Also, we can rearrange \(y = \frac{2}{5}x\) to solve for \(x\): multiply both sides by \(\frac{5}{2}\), we get \(x=\frac{5}{2}y\) (checking option D). Let's verify option A: If \(x = 200\), then \(y=\frac{2}{5}\times200 = 80\), which matches. For option D: If \(y = 80\), then \(x=\frac{5}{2}\times80=200\), which also matches. Option B: \(y=\frac{5}{2}x\) would give \(y=\frac{5}{2}\times200 = 500\), which is wrong. Option C: \(x=\frac{2}{5}y\) would give \(x=\frac{2}{5}\times80 = 32\), which is wrong.

Step2: Confirm the correct equations

So the equations that apply are \(y=\frac{2}{5}x\) (Option A) and \(x=\frac{5}{2}y\) (Option D).

Answer:

A. \(y = \frac{2}{5}x\)
D. \(x=\frac{5}{2}y\)