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Gavin wrote the equation [tex]p = \frac{3(s + 100)}{4}[/tex] to represent [tex]p[/tex], the profit he makes from [tex]s[/tex] sales in his lawn-mowing business.

Which equation is solved for [tex]s[/tex]?

A. [tex]s = \frac{4p - 300}{3}[/tex]
B. [tex]s = \frac{40 - 300}{3}[/tex]
C. [tex]s = \frac{4p}{300}[/tex]
D. [tex]s = \frac{400p}{3}[/tex]


Sagot :

To solve for [tex]\( s \)[/tex] in the given equation [tex]\( p = \frac{3(s + 100)}{4} \)[/tex], follow these steps:

1. Multiply both sides by 4 to eliminate the denominator:
[tex]\[ 4p = 3(s + 100) \][/tex]

2. Divide both sides by 3 to isolate the term with [tex]\( s \)[/tex]:
[tex]\[ \frac{4p}{3} = s + 100 \][/tex]

3. Subtract 100 from both sides to solve for [tex]\( s \)[/tex]:
[tex]\[ s = \frac{4p}{3} - 100 \][/tex]

Therefore, the equation solved for [tex]\( s \)[/tex] is:
[tex]\[ s = \frac{4p}{3} - 100 \][/tex]

Given the options, the correct equation for [tex]\( s \)[/tex] is not explicitly listed. However, the correct form based on our calculations is:
[tex]\[ s = \frac{4p}{3} - 100 \][/tex]