Example 13 - Chapter 7 Class 7 - Finding the Unknown (Ganita Prakash II)

Transcript

Example 13 Can you give a real-life situation that can be modelled as the equation, 100x + 75 = 250?This example asks us to connect a math equation to the real world. This is one of the most important skills in algebra! The equation is: 𝟏𝟎𝟎𝒙+𝟕𝟓=𝟐𝟓𝟎 To "solve" this example, we need to do two things: Create a Story: Describe a real-life situation that fits these numbers. Do the Math: Find the actual value of 𝑥. Creating the Story (The Real-Life Situation) To build a story, we need to understand what each part of the equation represents. Think of it like a receipt from a shop or a ride. 250 (The Total): This is the final amount you paid. 75 (The Fixed Constant): This is a cost that never changes. You pay it once, no matter what. (Examples: A delivery fee, a taxi base fare, or an entry fee). 100x (The Variable Part): This part changes based on 𝑥. 100 is the Rate (Cost per item or per km). 𝑥 is the Quantity (How many items or km). Here is a perfect real-life story for this equation: The Auto-Rickshaw Ride Imagine you take an auto-rickshaw to your friend's house. The driver charges a fixed "meter down" fee of ₹75 just for starting the ride. The ride costs ₹100 for every kilometer you travel. When you reach your destination, the total bill is ₹250. Question: How many kilometers ( 𝑥 ) did you travel? Doing the Math (Finding the value of 𝒙 ) Our equation is 100𝑥+75=250 Putting 75 to right side, it becomes subtraction 100x = 250 – 75 100x = 175 Putting 100 on right side, it becomes division x =175/100 x = 1.75 Thus, In our real-life story, this means you traveled exactly 𝟏.𝟕𝟓 kilometers.