An illustration shows insects, all the same size, shaded in two patterns. The first group of shaded insects is shown in two rows, with each row containing 5 insects. Next to these are two insects with a different shading than the first group.

Question

Identify the ratio of plain blue bugs to the total number of bugs.

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Answer 1

To determine the ratio of plain blue bugs to the total number of bugs, we first need to calculate the total number of bugs.

From your description:

• The first group has 2 rows with 5 insects each. So, there are \(2 \times 5 = 10\) shaded insects in the first group.
• Then, there are 2 additional insects with a different shading.

Now, adding these together, the total number of insects (both shaded and plain blue) is: \[ 10 \text{ (shaded insects)} + 2 \text{ (different shaded insects)} = 12 \text{ total insects} \]

Assuming the plain blue bugs are represented in the two shaded patterns, and that you intended for the 2 different shaded insects to be the plain blue bugs. This indicates we have:

• 2 plain blue bugs.

Now, the ratio of plain blue bugs to the total number of bugs is calculated as: \[ \text{Ratio} = \frac{\text{Number of plain blue bugs}}{\text{Total number of bugs}} = \frac{2}{12} \]

Simplifying this ratio gives: \[ \frac{2}{12} = \frac{1}{6} \]

Thus, the ratio of plain blue bugs to the total number of bugs is \( \frac{1}{6} \).