I have a bag with only red, blue, and green marbles.  The ratio of red marbles to blue marbles to green marbles is $1:5:3$.  There are 27 green marbles in the bag.  How many marbles are there  in the bag?
Since the ratio of red to blue to green marbles is $1:5:3$, the ratio of green marbles to the total number of marbles is $3/(1+5+3) = 3/9=1/3$.  Since the green marbles are one-third of the total, and there are 27 green marbles, there must be $3\cdot 27 = \boxed{81}$ total marbles.
81
Level 2
Prealgebra
Problem: I have a bag with only red, blue, and green marbles.  The ratio of red marbles to blue marbles to green marbles is $1:5:3$.  There are 27 green marbles in the bag.  How many marbles are there  in the bag?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the total number of marbles, we first need to determine the number of red and blue marbles based on the given ratio and the number of green marbles. The ratio of red to blue to green marbles is 1:5:3. This means for every 1 red marble, there are 5 blue marbles and 3 green marbles.

Let the number of red marbles be represented as \( r \), the number of blue marbles as \( b \), and the number of green marbles as \( g \). According to the ratio, we can express the number of marbles in terms of a common variable \( x \):

- \( r = 1x \)
- \( b = 5x \)
- \( g = 3x \)

We know from the problem that there are 27 green marbles, so we set \( g = 3x = 27 \). To find \( x \), we solve for \( x \):

\[
3x = 27
\]
\[
x = \frac{27}{3} = 9
\]

Now that we have \( x \), we can find the number of red and blue marbles:

- \( r = 1x = 1 \times 9 = 9 \)
- \( b = 5x = 5 \times 9 = 45 \)

Next, we calculate the total number of marbles in the bag by adding the number of red, blue, and green marbles together:

\[
\text{Total} = r + b + g = 9 + 45 + 27
\]

Calculating this gives:

\[
\text{Total} = 9 + 45 = 54
\]
\[
\text{Total} = 54 + 27 = 81
\]

Thus, the final answer is 81.<|END_OF_LATENT|> The final answer is $81$.