Solving Problems on Linear Equations One Variable Third Quarter Grade 8 Matatag Revised K-12 Math

The video introduces the topic of solving word problems using linear equations in one variable, including number, geometry, and money problems. It begins with a quick review of linear equations in one variable, defined as equations in the form ax + b = c, where a, b, and c are real numbers and a is not zero, with only one variable and a degree of one. Examples like 3x + 5 = 11 are provided. The presenter outlines five steps for solving word problems: understanding the problem, representing unknowns with a variable, translating conditions into an equation, solving the equation, and checking/interpreting the answer.

The first example tackles a number problem: 'The sum of two consecutive integers is 27. Find the numbers.' The steps are applied by letting the first number be 'x' and the second be 'x + 1'. The equation formed is x + (x + 1) = 27. Solving this equation leads to x = 13, making the two consecutive integers 13 and 14. The solution is then checked to ensure it satisfies the problem's conditions.

This example discusses finding two numbers where their difference is 45, and the larger number is five less than three times the smaller number. The smaller number is represented as 'x', and the larger number as '3x - 5'. The equation derived is (3x - 5) - x = 45. Solving this yields x = 25 for the smaller number, and the larger number is calculated to be 70. The solution is verified by checking if their difference is 45.

A geometry problem involving a rectangular playground with a 96m fence is presented. The length is 8m more than its width. The width is 'x', and the length is 'x + 8'. Since the fence encloses the playground, it refers to the perimeter, P = 2L + 2W. The equation is 96 = 2(x + 8) + 2x. Solving this equation, the width 'x' is found to be 20 meters, and the length is 28 meters. The answers are checked using the perimeter formula.

This geometry problem asks to find the measure of an angle where its supplement is 40 degrees more than twice its complement. The angle is 'x', its complement is '90 - x', and its supplement is '180 - x'. The equation formed is 180 - x = 40 + 2(90 - x). After solving, the angle 'x' is determined to be 40 degrees.

A money problem involving Anna and Beya, who have a total of 450 pesos. Anna has 90 pesos more than Beya. Beya's money is 'x', and Anna's is 'x + 90'. The equation is x + (x + 90) = 450. Solving for x, Beya has 180 pesos, and Anna has 270 pesos. The total amount is verified to be 450 pesos.

Lara's jar contains 50 and 100 peso bills totaling 4,250 pesos. The number of 50-peso bills is five more than twice the number of 100-peso bills. Let 'x' be the number of 100-peso bills. The number of 50-peso bills is '2x + 5'. The equation is 100x + 50(2x + 5) = 4250. Solving this, 'x' (number of 100-peso bills) is 20, and the number of 50-peso bills is 45.

An age problem: Carla's age is six less than twice Diane's age, and their combined age is 48. Diane's age is 'x', and Carla's age is '2x - 6'. The equation is x + (2x - 6) = 48. Solving for x, Diane is 18 years old, and Carla is 30 years old. Their total age is confirmed to be 48.

The final example is a motion problem. A bus leaves at 50 km/h, and 3 hours later, a van leaves the same terminal at 70 km/h. The goal is to find when the van will overtake the bus. Let 't' be the time the van travels. The bus travels for 't + 3' hours. Since distance = rate × time, the equation is 50(t + 3) = 70t. Solving this, 't' is 7.5 hours. So, the van will catch the bus after 7.5 hours of its travel.