Understanding Word Problems in Mathematics
Introduction
Assalamualikum dear students, today we are going to solve a word problem. In this article, we will be discussing a specific word problem where we need to determine the age of a woman based on certain given information. So let's dive right in!
The Problem
Our problem statement is as follows: "A woman is now three times as old as her son. In 10 years, the sum of their ages will be 76. How old was the woman when her son was born?"
Solution
Let's break down the problem step by step to find the solution.
Step 1: Determine the Current Ages
First, let's assign variables to the ages of the woman and her son. Let's represent the woman's age as 'w' and the son's age as 's'.
Based on the given information, we know that the woman is currently three times as old as her son. Therefore, we can write the equation: w = 3s.
Step 2: Calculate the Current Ages
Since we don't have the specific ages of the woman and her son, we need to work with the relative values. Let's assume the son's age is '1'. Using this assumption, we can calculate the woman's age.
Substituting the value of 's' as 1 in the equation w = 3s, we get w = 3(1) = 3.
Step 3: Determine the Future Ages
According to the problem, in 10 years, the sum of their ages will be 76. Let's calculate the future ages.
We add 10 years to both the woman's and son's current ages. The woman's age will be w + 10 and the son's age will be s + 10.
So, we can write the equation: (w + 10) + (s + 10) = 76.
Step 4: Solve the Equation
Now, let's solve the equation to find the ages of the woman and her son in the future.
Simplifying the equation, we get: w+ s + 20 = 76.
now substitute w=3s into the equation : 3s+s+20 = 76.
4s+20=76
subtract -76 from both sides; 4s+20-76=76-76
4s-56=0
4s=56
s=56/4
s=14/1
s=14
put s=14 in the equation we get W=3s
women=3 multiply by 14
women =42 ans
how old are women when her son was born to find this statement we have to minus son's age from women's age:
women=42-14
women=38
thus the women was 38 years old when her baby was born.
The correct answer is 38 years old. Ans!
Conclusion
Based on the given information and calculations, we have determined that the woman's age, when her son was born, is 38 years old. This problem showcases the application of algebraic equations to solve word problems in mathematics.
Keep Practicing!
Word problems can be challenging, but with practice, you can become proficient at solving them. Remember to break down the problem into smaller steps, assign variables, and solve the equations systematically. Keep practicing, and soon you'll excel at word problems!