Solving a Word Problem Involving Bakery Goods and Ratios

In a common math competition, you may encounter a scenario where you have to solve a problem involving bakery goods and ratios. Let's walk through a step-by-step solution to understand how to tackle such problems effectively.

The Problem Statement

A local bakery had 480 cupcakes and 300 muffins. After selling an equal number of cupcakes and muffins, the remaining number of cupcakes became 4 times the number of muffins left. The challenge is to determine how many muffins were sold.

Solving the Problem

Let's denote the number of cupcakes and muffins sold as x.

Initial Quantities

Initially, the bakery had:

Cupcakes: 480 Muffins: 300

Remaining Quantities

After selling x cupcakes and x muffins, the remaining quantities are:

Cupcakes left: 480 - x Muffins left: 300 - x

Setting Up the Equation

According to the problem, the number of cupcakes left is 4 times the number of muffins left. We can express this as:

480 - x 4(300 - x)

Solving the Equation

Distribute the 4 on the right side of the equation: 480 - x 1200 - 4x Add 4x to both sides to combine like terms: 480 3x 1200 Subtract 480 from both sides to isolate the term with x: 3x 720 Divide both sides by 3 to solve for x: x 240

This means that 240 muffins were sold.

Verification

To verify the solution, we can check the remaining quantities:

Cupcakes left: 480 - 240 240 Muffins left: 300 - 240 60

Checking the ratio:

240 4 * 60

The solution is correct, confirming that the number of muffins sold is indeed 240.

Conclusion

By following these steps, we can confidently solve word problems related to ratios and equal quantities in the context of bakery goods. Whether you are preparing for a math competition or solving a real-world problem, mastering these techniques will prove invaluable.