Question

reese has 152 full boxes of pairs of shoes and 7 loose pairs of shoes. if reese has a total of 1857 pairs of shoes, which equation can be
a. 7x + 152 = 1857
b. 7x - 152 = 1857
c. 152x + 7 = 1857
d. 152x - 7 = 1857

Explanation:

To solve this problem, we first need to understand the context. Let's assume the problem is about finding the number of pairs of shoes, where we have \( x \) full boxes (each with 12 pairs) and 7 loose pairs, and the total number of pairs is 1857.

Step 1: Analyze the situation

If each full box has 12 pairs of shoes, then \( x \) full boxes contain \( 12x \) pairs of shoes. We also have 7 loose pairs. The total number of pairs of shoes is the sum of the pairs from the full boxes and the loose pairs, which equals 1857.

Step 2: Set up the equation

The total number of pairs of shoes is given by the number of pairs in the boxes plus the loose pairs. So:

$$ 12x + 7 = 1857 $$

Step 3: Match with the options

Looking at the options:

• Option A: \( 12x + 12 = 1857 \) (incorrect, as we have 7 loose pairs, not 12)
• Option B: \( 12x - 12 = 1857 \) (incorrect, subtraction does not fit the context)
• Option C: \( 12x + 7 = 1857 \) (matches our derived equation)

So the correct equation is \( \boldsymbol{12x + 7 = 1857} \), which corresponds to option C.

Answer:

To solve this problem, we first need to understand the context. Let's assume the problem is about finding the number of pairs of shoes, where we have \( x \) full boxes (each with 12 pairs) and 7 loose pairs, and the total number of pairs is 1857.

Step 1: Analyze the situation

If each full box has 12 pairs of shoes, then \( x \) full boxes contain \( 12x \) pairs of shoes. We also have 7 loose pairs. The total number of pairs of shoes is the sum of the pairs from the full boxes and the loose pairs, which equals 1857.

Step 2: Set up the equation

The total number of pairs of shoes is given by the number of pairs in the boxes plus the loose pairs. So:

$$ 12x + 7 = 1857 $$

Step 3: Match with the options

Looking at the options:

• Option A: \( 12x + 12 = 1857 \) (incorrect, as we have 7 loose pairs, not 12)
• Option B: \( 12x - 12 = 1857 \) (incorrect, subtraction does not fit the context)
• Option C: \( 12x + 7 = 1857 \) (matches our derived equation)

So the correct equation is \( \boldsymbol{12x + 7 = 1857} \), which corresponds to option C.