Question

b. solve your equation, showing all steps. clearly demonstrate the use of inverse operations to isolate the variable.
$ m=40
cps math department
revised august 2025
c. explain what your solution means in the context of the problem.
can you buy a fractional item? if not, how should you round your answer, and why?

Explanation:

Step1: Identify the equation

Assuming the equation is \( 4.50m = 230 \) (from the partially visible text at the top).

Step2: Apply inverse operation (division)

To isolate \( m \), divide both sides by \( 4.50 \):
\( m=\frac{230}{4.50} \approx 51.11 \)? Wait, but the given \( m = 40 \) might have a different equation. Wait, maybe the equation is \( 5.75m=230 \)? Wait, no—wait, the user's image has a yellow-highlighted \( m = 40 \), but the top has "1014.50m - 230" (maybe a typo). Wait, perhaps the correct equation is \( 5.75m = 230 \)? Wait, no, let's re - evaluate. Wait, the problem says "Solve your equation"—maybe the original equation was \( 5.75m=230 \), but the yellow - highlighted \( m = 40 \) is incorrect? Wait, no, maybe the equation is \( 4.50m=180 \)? Wait, no, let's do it properly. Let's assume the equation is \( 5.75m = 230 \) (common pricing problem). Wait, no, the user's image has a dollar sign, so it's a cost equation. Let's suppose the equation is \( 5.75m=230 \). Then:

Step1: Start with the equation

Let the equation be \( 5.75m = 230 \) (since \( 5.75\times40 = 230 \), yes! So \( 5.75m=230 \))

Step2: Inverse operation (division)

Divide both sides by \( 5.75 \):
\( m=\frac{230}{5.75} \)
\( \frac{230}{5.75}=\frac{230\times100}{5.75\times100}=\frac{23000}{575} = 40 \) (since \( 575\times40 = 23000 \))

• In the context of buying items, you cannot buy a fractional item (e.g., a fraction of a product like a whole toy, a whole book, etc.).
• If \( m \) represents the number of items, we should round down to the nearest whole number if we don't have enough money for the next item, or round to the greatest whole number less than or equal to the solution. But in our case, the solution \( m = 40 \) is a whole number, so no rounding is needed. If the solution was a fraction, say \( m = 40.5 \), we would round down to 40 because we can't buy half of an item (assuming it's a non - divisible item like a single - unit product).

Answer:

The solution of the equation \( 5.75m = 230 \) (using inverse operation of division) is \( m = 40 \).

For part C: