To determine what [tex]\( p \)[/tex] represents in the equation [tex]\( 45p = 270 \)[/tex], let's break down the problem step by step.
1. Understand the Given Equation:
The equation is [tex]\( 45p = 270 \)[/tex]. Here, [tex]\( 45 \)[/tex] represents the cost of one pair of pants in dollars, and [tex]\( 270 \)[/tex] represents the total amount of money spent by the shopper.
2. Rewriting the Equation:
The equation can be interpreted as:
[tex]\[
\text{cost per pant} \times \text{number of pairs of pants} = \text{total amount spent}
\][/tex]
In this case, the cost per pant is [tex]\( \$45 \)[/tex], and the total amount spent is [tex]\( \$270 \)[/tex].
3. Solve for [tex]\( p \)[/tex]:
To find [tex]\( p \)[/tex], we need to isolate [tex]\( p \)[/tex] on one side of the equation.
[tex]\[
45p = 270
\][/tex]
Divide both sides of the equation by [tex]\( 45 \)[/tex] to solve for [tex]\( p \)[/tex]:
[tex]\[
p = \frac{270}{45}
\][/tex]
Simplifying the division:
[tex]\[
p = 6
\][/tex]
4. Interpret [tex]\( p \)[/tex]:
From the equation solving process, we deduced that [tex]\( p \)[/tex] is [tex]\( 6 \)[/tex]. Since [tex]\( 45p \)[/tex] represents the total amount spent, [tex]\( p \)[/tex] equals the number of pairs of pants purchased.
Thus, [tex]\( p \)[/tex] represents the total number of pairs of pants the shopper purchased.
So, the correct interpretation is:
- The total number of pairs of pants the shopper purchased
