The Problem: The ratio of blocks A:B:C:D is in the ratio of 4:7:3:1. If the number of A blocks is 50 more than the number of C blocks, what is the number of B blocks?

Solution with Step-by-Step Explanation

We are given that the ratio of blocks A:B:C:D is 4:7:3:1. This can be represented as A, B, C, and D being 4x, 7x, 3x, and x, respectively, where x is a common factor.

Step 1: Understanding the Given Information

The number of A blocks is 50 more than the number of C blocks. This can be written as:

4x - 3x 50.

Step 2: Solving for x

By simplifying the equation:

4x - 3x 50

x 50

Step 3: Finding the Number of B Blocks

Since the number of B blocks is 7x, we substitute the value of x to find the number of B blocks:

B 7x 7 * 50 350.

Therefore, the number of B blocks is 350.

Alternative Approach

Step 1: Setting Up the Ratios

Let the ratio be A:B:C:D as 4:7:3:1. We can write the numbers of blocks as:

A 4x, B 7x, C 3x, D x.

Step 2: Using the Given Condition

The number of A blocks is 50 more than the number of C blocks. This gives us:

4x - 3x 50.

Step 3: Solving for x Again

By solving the equation:

4x - 3x 50

x 50

Step 4: Finding the Number of B Blocks

Since B 7x, we substitute the value of x to find the number of B blocks:

B 7x 7 * 50 350.

Therefore, the number of B blocks is 350.

Conclusion

The problem is solved using the concept of ratios and algebra. By setting up the equations and solving for the common factor, we were able to determine the number of B blocks. The final answer is 350.

References

1. Ratios and Proportions: Math is Fun

2. Basic Algebra: Khan Academy