Question

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 plain insects. Next to these are two insects with a different shading than the first group.
Identify the ratio of plain blue bugs to the total number of bugs.

Answer 1

To find the ratio of plain blue bugs to the total number of bugs, we can first count the bugs based on the information provided:

1. There are 10 plain insects (5 in the first row and 5 in the second row).
2. There are 2 insects with a different shading.

Therefore, the total number of bugs is:

\[
\text{Total bugs} = \text{Plain insects} + \text{Shaded insects} = 10 + 2 = 12
\]

Now, to find the ratio of plain blue bugs (which are the 10 plain insects) to the total number of bugs:

\[
\text{Ratio} = \frac{\text{Number of plain bugs}}{\text{Total number of bugs}} = \frac{10}{12}
\]

To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:

\[
\frac{10}{12} = \frac{5}{6}
\]

Thus, the ratio of plain blue bugs to the total number of bugs is:

\[
\boxed{\frac{5}{6}}
\]