Question

12 a company uses the formula $t = 581s + 150p$ to determine the total cost to purchase $s$ computers and $p$ printers. which formula can be used to determine the number of printers purchased, given the total cost, $t$, and the number of computers purchased? a $p = \frac{t}{150} - 581s$ b $p = t - \frac{581s}{150}$ c $p = \frac{t - 581s}{150}$ d $p = t - 581s - 150$

Explanation:

Step1: Start with the given formula

We have the total cost formula \( T = 581s + 150p \). Our goal is to solve for \( p \) in terms of \( T \) and \( s \).

Step2: Isolate the term with \( p \)

Subtract \( 581s \) from both sides of the equation. This gives us \( T - 581s = 150p \). The reasoning here is that we want to get the term containing \( p \) (which is \( 150p \)) by itself on one side of the equation, so we perform the inverse operation of addition (subtraction) on \( 581s \).

Step3: Solve for \( p \)

Now, divide both sides of the equation \( T - 581s = 150p \) by \( 150 \) to solve for \( p \). When we divide both sides by \( 150 \), we get \( p=\frac{T - 581s}{150} \). This is because to isolate \( p \), we need to perform the inverse operation of multiplication (division) on the coefficient of \( p \), which is \( 150 \).

Answer:

C. \( p=\frac{T - 581s}{150} \)