How to Divide 33 Photos into Two Groups with a Ratio of 4 to 7

Dividing a collection of 33 photos into two groups with a specific ratio can be achieved through a series of mathematical calculations. This guide will detail the method for achieving the desired ratio of 4 to 7 between the two groups.

Understanding the Ratio and Total Number of Photos

The total number of photos to be divided is 33. The desired ratio is 4 to 7, which means that for every 4 photos in one group, there should be 7 photos in the other group. This can be represented as a ratio of 4:7.

Expressing the Groups in Terms of a Variable

Let's denote the number of photos in the first group as x and the number of photos in the second group as y. The sum of those two groups should equal the total number of photos:

x y 33

Furthermore, the ratio of the first group to the second group should be 4:7:

x / y 4 / 7

Solving the Problem

To find the values of x and y, we can solve these two equations simultaneously:

Step 1: Express y in terms of x

From the ratio equation:

x / y 4 / 7 can be rearranged to:

y 7x / 4

Step 2: Substitute y in the Total Photos Equation

Substitute y 7x / 4 into the equation x y 33:

x 7x / 4 33

To combine the terms, we need a common denominator:

(4x 7x) / 4 33

Simplify the left side:

11x / 4 33

Multiply both sides by 4:

11x 132

Divide by 11:

x 12

Step 3: Calculate y

Now, using x to find y:

y 7x / 4 7 × 12 / 4 21

So, the first group should contain 12 photos, and the second group should contain 21 photos.

Verification

To verify, we can check that the total number of photos is 33:

12 21 33

And the ratio is 4:7:

12 / 21 4 / 7

Alternative Methods

For those who prefer not to perform the arithmetic calculation, an alternative method involves visualizing the distribution using a table or simply moving the photos step by step.

Start by spreading the photos out on a table. Move the photos one by one, moving four to the left and seven to the right. Repeat this process until all photos are distributed according to the 4:7 ratio.

Conclusion

This method is useful for solving similar math problems, particularly those involving the division of objects or resources into specific ratios. Understanding the fundamental principles behind the calculations can help in solving a wide range of similar problems.

By following the steps outlined above, you can efficiently divide any number of items into two groups with a given ratio, without the need for complex calculations.