Multiple Choice Question

Janice has a pasta recipe that calls for 2 ounces of cheese for every 3 ounces of cooked pasta. Which graph shows this relationship between cheese and pasta?
A.
The graph showing 'pasta' from 0 to 10 along the x-axis and 'cheese' from 0 to 10 along the y axis showing a upward facing line starting (0, 0) and passing through the points (2, 3), (4, 6) and (6, 9).

B.
The graph showing 'pasta' from 0 to 10 along the x-axis and 'cheese' from 0 to 10 along the y axis showing a upward facing line starting (0, 0) and passing through the points (3, 2), (6, 4), and (9, 6).

C.
The graph showing 'pasta' from 0 to 10 along the x-axis and 'cheese' from 0 to 10 along the y axis showing a upward facing line starting (0, 0) and passing through the points (2, 2), (4, 4), (6, 6), (8, 8) and (10, 10).

D.
The graph showing 'pasta' from 0 to 10 along the x-axis and 'cheese' from 0 to 10 along the y axis showing a upward facing line starting (0, 0) and passing through the points (5, 2) and (10, 4).

1 answer

To find the correct graph that represents the relationship between cheese and cooked pasta based on the given ratio (2 ounces of cheese for every 3 ounces of cooked pasta), we should analyze the ratio.

The relationship can be expressed as:

\[ \text{cheese} = \frac{2}{3} \times \text{pasta} \]

This means that for every 3 ounces of pasta, you need 2 ounces of cheese. We can calculate some points using this ratio:

  • If pasta = 0 ounces, cheese = \( \frac{2}{3} \times 0 = 0 \) ounces.
  • If pasta = 3 ounces, cheese = \( \frac{2}{3} \times 3 = 2 \) ounces.
  • If pasta = 6 ounces, cheese = \( \frac{2}{3} \times 6 = 4 \) ounces.
  • If pasta = 9 ounces, cheese = \( \frac{2}{3} \times 9 = 6 \) ounces.

Now, let's evaluate the given graph options:

  • Option A: The line passes through (2, 3), (4, 6), and (6, 9). This suggests a ratio of 3 ounces of pasta for every 2 ounces of cheese; this is incorrect.

  • Option B: The line passes through (3, 2), (6, 4), and (9, 6). This follows the correct ratio of 2 ounces of cheese for every 3 ounces of pasta. This option is correct.

  • Option C: The line passes through points that suggest a 1:1 ratio which does not match the given ratio; this is incorrect.

  • Option D: The pairs (5, 2) and (10, 4) suggest a different ratio that does not match the specified needs; this is incorrect.

The right choice is B, which correctly represents the relationship between cheese and pasta using the specified ratio of 2 ounces of cheese for every 3 ounces of cooked pasta.