Question

During a musical an orchestra is playing. As the music plays, the volume changes in the beginning of the piece can be modeled by the equation s = 10│x - 4│+ 50 where s represents the sound level in decibels and x represents the number of measures of music played. Explain in words each step to find the following question:
At what number(s) measures played would the sound level be at 80 decibels?

Answer 1

Answer:

The numbers of measure of music played are 1 and 7

Step-by-step explanation:

Given

$s = 10|x - 4| + 50$

Required

Solve for x when s = 80

Substitute 80 for x

$80 = 10|x - 4| + 50$

Subtract 50 from both sides

$80 - 50= 10|x - 4| + 50 - 50$

$30= 10|x - 4|$

Divide through by 10

$\frac{30}{10}= \frac{10|x - 4| }{10}$

$3= |x - 4|$

Reorder

$|x - 4| = 3$

This can be split into

$x - 4 = 3$ or $x - 4 = -3$

Solve for x

$x = 4 + 3$ or $x = 4 - 3$

$x = 7$ or $x = 1$

Hence:

The numbers of measure of music played are 1 and 7