Question

Veronica is filling a bag with marbles. She fills the bag with 8 green marbles for every 6 red marbles. The table below shows the numbers of green and red marbles she used.

Green Marbles Red Marbles
8 6
12 9
16 12
20 15

Using the information from the table, choose the correct statement.
A.
There are 4 green marbles, for every 3 red marbles.
B.
The ratio of the number of green marbles to the total number of marbles is 4:3.
C.
The ratio of the number of red marbles to the total number of marbles is 7:3.
D.
For each red marble, there are 2 green marbles.

Answer 1

Let's analyze the options based on the ratio of green and red marbles provided.

From the problem, we see that for every 8 green marbles, there are 6 red marbles, which implies the ratio of green to red marbles is:

\[
\text{Ratio of Green to Red} = \frac{8}{6} = \frac{4}{3}
\]

Now we can evaluate each statement:

**A. There are 4 green marbles for every 3 red marbles.**
- This statement is correct based on the simplified ratio we derived (4:3).

**B. The ratio of the number of green marbles to the total number of marbles is 4:3.**
- Total marbles for the smallest example (8 green and 6 red) is \( 8 + 6 = 14 \).
- The ratio of green marbles to total marbles is \( \frac{8}{14} = \frac{4}{7} \).
- This statement is incorrect.

**C. The ratio of the number of red marbles to the total number of marbles is 7:3.**
- Using 8 green and 6 red, total is 14. The ratio of red marbles would be \( \frac{6}{14} = \frac{3}{7} \).
- This statement is incorrect.

**D. For each red marble, there are 2 green marbles.**
- The ratio of red to green is \( \frac{6}{8} = \frac{3}{4} \). So, for each red marble there are \( \frac{8}{6} = \frac{4}{3} \) green marbles.
- This statement is incorrect as it suggests there are 2 green marbles for each red marble.

Thus, the correct statement is:

**A. There are 4 green marbles for every 3 red marbles.**