The ratio of the loudness of Lala’s earphones to the loudness of Polina’s
earphones to the loudness of Goffy’s earphones is 6 : 5: 3, respectively.
If Polina’s earphones have a loudness of 90 decibels, find the total
loudness of all three earphones.
252 decibles
252
To find the total loudness of all three earphones, we need to first determine the loudness of Lala's earphones and Goffy's earphones.
Given that the ratio of loudness is 6:5:3, and we know the loudness of Polina's earphones is 90 decibels, we can set up a proportion to find the loudness of Lala's and Goffy's earphones.
Let's assume the loudness of Lala's earphones is 6x, where x is a constant. And the loudness of Goffy's earphones is 3x.
Now, we can set up the proportion: (Polina's loudness) / (Lala's loudness) = 90 / 6x.
Cross-multiplying, we get 90 * Lala's loudness = 6x * 90.
Simplifying the equation, we have Lala's loudness = 540 / 6x = 90/ x.
Similarly, we can set up a proportion to find Goffy's loudness: (Polina's loudness) / (Goffy's loudness) = 90 / 3x.
Cross-multiplying, we get 90 * Goffy's loudness = 3x * 90.
Simplifying the equation, we have Goffy's loudness = 270 / 3x = 90 / x.
Now that we know the loudness of each person's earphones, we can add them together to find the total loudness.
Total loudness = Polina's loudness + Lala's loudness + Goffy's loudness
= 90 + (90/x) + (90/x)
= 90 + 180/x
Note: Since we don't have a specific value for x, we cannot provide an exact numerical answer. However, we can express the total loudness as a function of x, which represents the constant in the proportion.
90/5 = 18, so
6:5:3 = 108:90:54
now finish it off