Question

The shapes show that there are 4 squares for every

6 circles and 4 squares.
4 circles.
6 circles.
8 circles.
10 circles.

Answer 1

To determine the relationship indicated by "4 squares for every," we can express it as a ratio. If there are 4 squares, then based on the provided options to complete the sentence, we can analyze the relationships involving the circles.

Let's denote:
- Let \( S \) represent squares.
- Let \( C \) represent circles.

The ratio of squares to circles is given as \( S:C \). According to the statement, we have:

\[
S = 4
\]

Now, we know that this corresponds to certain quantities of circles. The options provided suggest different possible ratios:

1. **6 circles and 4 squares**: This suggests a ratio of \( 4:6 \), which simplifies to \( 2:3 \). This works out because if we take scales, we can multiply the squares by \( 1.5 \) to get \( 6 \) and circles by \( 1.5 \) to get \( 9 \), maintaining the ratio.

2. **4 circles**: This implies the ratio of \( 4:4 \), simplifying to \( 1:1 \), which does not correspond to the given ratio.

3. **6 circles**: This implies the same as option 1, giving a ratio of \( 4:6 \) or \( 2:3 \).

4. **8 circles**: This gives us the ratio of \( 4:8 \), which simplifies to \( 1:2 \), again not corresponding to the initial ratio.

5. **10 circles**: This gives us the ratio of \( 4:10 \), simplifying to \( 2:5 \), which also does not correspond to the initial ratio.

Considering this analysis, the best option that reflects the original ratio of squares and circles is:

**6 circles and 4 squares.**

Thus, the complete sentence is: "There are 4 squares for every 6 circles."