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The problem you provided states:

The ratio of the loudness of Lala's earphones to Polina's earphones to Geoff's earphones is 6:5:3. If Polina's earphones have a loudness of 90 decibels, find the total loudness of all three earphones.

### Solution:

Let the loudness of Lala's, Polina's, and Geoff's earphones be represented by \(6x\), \(5x\), and \(3x\) respectively, based on their given ratio of 6:5:3.

We know that the loudness of Polina's earphones is 90 decibels. Therefore, we set:

\[
5x = 90
\]

Solving for \(x\):

\[
x = \frac{90}{5} = 18
\]

Now, we can find the loudness of Lala's and Geoff's earphones:

- Lala's earphones: \(6x = 6 \times 18 = 108\) decibels
- Geoff's earphones: \(3x = 3 \times 18 = 54\) decibels

### Total loudness:
The total loudness of all three earphones is:

\[
108 + 90 + 54 = 252 \text{ decibels}
\]

Thus, the total loudness is **252 decibels**.

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Here are some related questions you might find interesting:

1. If Geoff's earphones had a loudness of 54 decibels, what would Polina's earphone loudness be?
2. What would the loudness ratio be if Geoff's earphones were 20 decibels louder than Polina's?
3. If the loudness of Polina's earphones was increased by 10%, what would the new total loudness be?
4. How does changing one person's loudness by a factor of 2 affect the total loudness?
5. If the total loudness was 500 decibels, what would the individual loudness levels be?

**Tip**: In problems involving ratios, it’s useful to assign variables to unknown quantities and solve step by step!

The ratio of the loudness of Lala's earphones to the loudness of Polina's earphones to the loudness of Geoff's earphones is 6:5:3. If Polina's earphones have a loudness of 90 decibels, find the total loudness of all three earphones.

Learn how to calculate the total loudness of earphones when given the ratio of loudness for three different earphones. This problem covers fundamental mathematical concepts such as ratios, proportions, and algebra. Suitable for students in Grades 6-8.

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