Question

project tasks:
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.
b. solve your equation, showing all steps. clearly demonstrate the use of inverse operations to isolate the variable.

Explanation:

Step1: Define variables and equation

Let \( m \) be the number of mystery items. The total budget is \(\$250\), and \(\$70\) is spent on fixtures. The cost of each mystery item is \(\$4.50\). So the equation is: \( 70 + 4.50m = 250 \)

Step2: Subtract 70 from both sides

Subtract 70 from each side to isolate the term with \( m \): \( 70 + 4.50m - 70 = 250 - 70 \)
Simplify: \( 4.50m = 180 \)

Step3: Divide by 4.50

Divide both sides by 4.50 to solve for \( m \): \( \frac{4.50m}{4.50} = \frac{180}{4.50} \)
Simplify: \( m = 40 \)

Answer:

A. The two - step linear equation is \( 70+4.50m = 250 \)
B. The number of mystery items \( m = 40 \)