The relationship between the volume and mass of the soup is proportional, which means we can set up a proportion based on the values given.
From the problem, we know:
- A 290 mL serving has a mass of 180 g.
We can write a proportion to find the mass (m) of a 348 mL serving:
\[ \frac{180 , \text{g}}{290 , \text{mL}} = \frac{m , \text{g}}{348 , \text{mL}} \]
To find \( m \), we can cross-multiply:
\[ 180 , \text{g} \times 348 , \text{mL} = m , \text{g} \times 290 , \text{mL} \]
Now, calculate \( 180 \times 348 \):
\[ 180 \times 348 = 62,640 \]
Now, we will set up the equation:
\[ 62,640 = m \times 290 \]
Now, solve for \( m \):
\[ m = \frac{62,640}{290} \]
Now perform the division:
\[ m \approx 216 , \text{g} \]
Therefore, the mass of a 348 mL serving of soup is approximately 216 g.