SOLVING PROBLEMS INVOLVING RATIO AND PROPORTION || GRADE 9 MATHEATICS Q3

Introduction to Ratio and Proportion Problems00:00:12

The video introduces the objective of solving problems involving ratio and proportion.

Example 1: Proportional Height in a Photograph00:00:22

This example calculates Argyle's actual height given Anne's height in a photograph and her actual height, assuming proportionality. The problem sets up the ratio 9/10 = 153/X and solves for X, finding Argyle's actual height to be 170 centimeters. The solution is verified by cross-multiplication.

Example 2: Recipe Scaling with Proportion00:02:28

This problem involves scaling a grilled teriyaki pork recipe. If 1 kilo of pork serves 4 people, the video calculates how much pork is needed to serve 20 people. Setting up the proportion 1/4 = X/20, the solution determines that 5 kilos of pork are required. The answer is checked by cross-multiplication.

Example 3: Checking Proportionality of Photo Sizes00:03:50

The video examines whether two photo dimensions (13cm x 9cm and 15cm x 10cm) are proportional. By setting up the ratio 13/9 = 15/10 and cross-multiplying, it is found that 130 is not equal to 135, indicating the dimensions are not proportional.

Example 4: Ratio of Boys to Girls in a Club00:05:15

Given a ratio of boys to girls in a mathematics club of 4:5 and 25 girls, the problem aims to find the number of boys. The proportion 4/5 = X/25 is used to find X, which is 20, meaning there are 20 boys in the club. The solution is confirmed by cross-multiplication.

Example 5: Ratio of Letters in Words00:06:36

This example discusses a 5:3 ratio of letters between two words. If the first word has 15 letters, the number of letters in the second word is determined using the proportion 5/3 = 15/X, resulting in X = 9 letters. The answer is verified by cross-multiplication.

Example 6: Angles of a Triangle in a Ratio00:08:04

The measures of the three angles of a triangle are in the ratio 2:3:4. The video explains how to find the measure of each angle by representing them as 2x, 3x, and 4x. Since the sum of angles in a triangle is 180 degrees, 2x + 3x + 4x = 180, leading to x = 20 degrees. The angles are then calculated as 40, 60, and 80 degrees, and their sum is checked.

Example 7: Perimeter of a Triangle with Proportional Sides00:10:10

With a triangle perimeter of 90 centimeters and side lengths in the ratio 6:5:4, the task is to find the length of the shortest side. The sides are represented as 4x, 5x, and 6x. Their sum (4x + 5x + 6x = 90) yields 15x = 90, so x = 6. The lengths are 24, 30, and 36 centimeters, with the shortest side being 24 centimeters. The perimeter is checked by summing the side lengths.