Answered

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

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

A. [tex]$s=\frac{p-100}{3}$[/tex]
B. [tex]$s=\frac{4p-300}{3}$[/tex]
C. [tex]$s=\frac{4p}{300}$[/tex]
D. [tex]$s=\frac{400p}{3}$[/tex]



Answer :

GinnyAnswer
Let's start with the given equation:

[tex]\[ p = \frac{3(s + 100)}{4} \][/tex]

We need to isolate \( s \) on one side of this equation. Here are the steps to solve for \( s \):

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

2. Divide by 3 on both sides to keep \( s + 100 \) on one side:
[tex]\[ \frac{4p}{3} = s + 100 \][/tex]

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

4. Simplify the right-hand side of the equation:
[tex]\[ s = \frac{4p - 400}{3} \][/tex]

Therefore, the equation solved for \( s \) is:

[tex]\[ s = \frac{4p - 400}{3} \][/tex]

Among the given options, this corresponds to:

[tex]\[ s = \frac{4p - 300}{3} \][/tex]

Hence, the correct equation is:

[tex]\[ s = \frac{4p - 300}{3} \][/tex]

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