Sure! Let's break down the problem step by step to find Imran's present age.
1. Define the variables:
- Let [tex]\( x \)[/tex] be Imran's present age.
- Let [tex]\( y \)[/tex] be his cousin's present age.
2. Set up the equations based on the given information:
- The sum of their ages is given as 38. So, we have:
[tex]\[
x + y = 38
\][/tex]
- Seven years ago, Imran was thrice as old as his cousin. Seven years ago, Imran's age was [tex]\( x - 7 \)[/tex], and his cousin's age was [tex]\( y - 7 \)[/tex]. This gives us the equation:
[tex]\[
x - 7 = 3(y - 7)
\][/tex]
3. Simplify the second equation:
- Expand and simplify the second equation:
[tex]\[
x - 7 = 3y - 21
\][/tex]
[tex]\[
x - 3y = -14
\][/tex]
4. Solve the system of linear equations:
- We now have two equations:
1. [tex]\( x + y = 38 \)[/tex]
2. [tex]\( x - 3y = -14 \)[/tex]
- Solve the first equation for [tex]\( x \)[/tex]:
[tex]\[
x = 38 - y
\][/tex]
- Substitute [tex]\( x = 38 - y \)[/tex] into the second equation:
[tex]\[
(38 - y) - 3y = -14
\][/tex]
- Simplify:
[tex]\[
38 - 4y = -14
\][/tex]
[tex]\[
38 + 14 = 4y
\][/tex]
[tex]\[
52 = 4y
\][/tex]
- Solve for [tex]\( y \)[/tex]:
[tex]\[
y = \frac{52}{4} = 13
\][/tex]
5. Find Imran's present age:
- Substitute [tex]\( y = 13 \)[/tex] back into the equation [tex]\( x + y = 38 \)[/tex]:
[tex]\[
x + 13 = 38
\][/tex]
[tex]\[
x = 38 - 13
\][/tex]
[tex]\[
x = 25
\][/tex]
Therefore, Imran's present age is 25 years old.
