Applications of Simple Equations to Practical Situations
Transitioning from learning how to formulate and solve simple equations to applying these skills to solve real-world problems and puzzles is a crucial step in understanding mathematics. Here's a concise overview of this process:
Identify the Scenario: Recognize the practical situation or problem you're facing.
Translate into Equations: Convert the everyday language of the scenario into mathematical equations. This involves identifying the key elements of the situation and how they relate to each other in a mathematical sense.
Solve the Equations: Apply your knowledge of solving simple equations to find the solution to these real-world problems.
Interpret the Results: Make sure the solutions you find are meaningful within the context of the original problem.
Let's try this out now!
Example 8: The sum of three times a number and 11 is 32. Find the number.
Solution:
If the unknown number is taken to be x, then three times the number is 3x and the sum of 3x and 11 is
That is,
To solve this equation, we transpose
3x = 32 – 11 (or) 3x =
Now,
So, x =
The required number is 7.
Validation: We may check it by taking 3 times 7 and adding 11 to it. It gives 32 as required.
Example 9: Find a number, such that one-fourth of the number is 3 more than 7.
Solution:
Let us take the unknown number to be y; one-fourth of y is
This number (
Hence, we get the equation for y as
To solve this equation, first transpose 7 to RHS We get,
We then multiply both sides of the equation by
Example 10: Raju’s father’s age is 5 years more than three times Raju’s age. Find Raju’s age, if his father is 44 years old.
Let's denote Raju's age as r. Thus, three times of Raju's age is
And five years more than three times Raju's age is:
We have been given that this equation is equal to
Thus, the equation becomes:
= To solve, we subtract
from the RHS giving us RHS = Then we transpose 3 by
r from the RHS. We get: r =
Therefore, Raju is 13 years old.
There are two types of boxes containing mangoes. Each box of the larger type contains 4 more mangoes than the number of mangoes contained in 8 boxes of the smaller type. Each larger box contains 100 mangoes. Find the number of mangoes contained in the smaller box?
- Let x represent the number of mangoes in each small box.
- The number of mangoes in 8 small boxes is:
- The number of mangoes in a large box is 4 more mangoes than the number contained in 8 smaller boxes. This gives the equation:
- We know that the numerical value of the mangoes in the larger box is
- This gives the equation:
= - Solving, we transpose 4 by
from RHS, giving us RHS = - Now,
both sides of the equation by 8 to find the value of x - We find x =
- Thus, the number of mangoes in each small box is 12.
Q1
Q1(i) When you multiply a number by 6 and subtract 5 from the product, you get 7. Can you tell what the number is?
Solution:
Finding the number when multiplied by 6 and subtracting 5 from the product equals 7:
Set up the equation: Let the number be 'x'.
Solve for x:
Add 5 to both sides:
6x =
Divide by 6: x =
So, the number is x = 2.
Q2
Q1(ii) What is that number one third of which added to 5 gives 8?
Solution:
Finding the number one-third of which added to 5 gives 8:
Set up the equation: Let the number be 'x'.
Solve for x:
Subtract 5 from both sides:
Multiply by 3: x =
So, the number is x = 9.