Question

part 1: initial setup costs
youve been given a total budget of $250 to get the store ready. youve already spent $70 on permanent fixtures (like shelves, a display case, and a cash register). the remaining money needs to be used to buy your first batch of \mystery\ starter inventory items, which each cost the same amount.

1. equation & solution: if each mystery item costs $4.50, how many mystery items (m) can you buy?

a. write a two - step linear equation that represents this situation.
\t\t\t\t\t\t\t70 + 4.50m = 250
b. solve your equation, showing all steps. clearly demonstrate the use of inverse operations to isolate the variable.
\t\t\t\t\t\t\t? m = 40

Explanation:

Step1: Subtract 70 from both sides

To isolate the term with \( m \), we use the inverse operation of addition (subtraction). Subtract 70 from both sides of the equation \( 70 + 4.50m = 250 \):
\( 70 + 4.50m - 70 = 250 - 70 \)
Simplifying both sides gives:
\( 4.50m = 180 \)

Step2: Divide by 4.50

Next, use the inverse operation of multiplication (division) to solve for \( m \). Divide both sides by 4.50:
\( \frac{4.50m}{4.50} = \frac{180}{4.50} \)
Simplifying both sides gives:
\( m = 40 \)

Answer:

\( m = 40 \) (You can buy 40 mystery items.)