Math Problem Statement

3 erasers cost $4.41. Which equation would help determine the cost of 4 erasers? Choose 1 answer: A 4/x = $4.41 3 B 4 $4.41 = x/3 4/3 = $4.41 x D 4/x = 3 $4.41 E None of the above

Solution

To find the cost of 4 erasers based on the price of 3 erasers, you can use the relationship between the number of erasers and their total cost. The ratio of cost to the number of erasers should be the same for both 3 and 4 erasers.

Let's break this down:

  • For 3 erasers, the cost is $4.41, so the cost per eraser is 4.413\frac{4.41}{3}.
  • For 4 erasers, let the cost be xx, which means the cost per eraser is x4\frac{x}{4}.

Since the cost per eraser remains constant, the equation is:

4.413=x4\frac{4.41}{3} = \frac{x}{4}

This equation simplifies to:

4×4.41=x×34 \times 4.41 = x \times 3

Which matches option B: 4×4.41=x34 \times 4.41 = \frac{x}{3}.

Thus, the correct answer is B.

Would you like more details or have any questions about this?

Here are 5 related questions to expand on this concept:

  1. How do you solve for xx in the equation 4×4.41=x34 \times 4.41 = \frac{x}{3}?
  2. What is the cost of one eraser based on the given price of 3 erasers?
  3. How would the equation change if the price for 5 erasers was given instead of 3?
  4. Can you derive the formula for the cost of any number of erasers using the information given?
  5. How does this problem relate to finding unit rates in real-life situations?

Tip: When dealing with proportional relationships, finding the unit rate (cost per single item) can simplify solving for other quantities.

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Math Problem Analysis

Mathematical Concepts

Proportions
Ratios
Basic Algebra

Formulas

Cost per eraser = Total cost / Number of erasers
Proportion: (Cost for 3 erasers / 3) = (Cost for 4 erasers / 4)

Theorems

Proportionality Theorem

Suitable Grade Level

Grades 6-8