University:
University of Cambridge
Course:
0580 IGCSE | Mathematics
Academic year:

2023
Views:

259

Pages:

3
Author:

Shahbaz A.

Q65 Algebra Word Problems Packet No 1 shahbaz ahmed August 2024 Q 65.The total of the ages of three students is 38. If the youngest student is 7 years younger than the oldest student, and the middle student is 4 years older than the youngest student, how old is each student? Solution Let the oldest student in age= x years. 7 years younger than the oldest student=x-7 years. The age of the the youngest student= x-7 years 4 years older than the youngest student= x-7+4=x-3 years. The age of the middle student= x-3 years. The total of the ages of three students= x+x-7+x-3=3x-10 The total of the ages of three students = 38. According to the condition 1 3x − 10 = 38 3x − 10 + 10 = 38 + 10 3x = 48 x= 48 3 x = 16 years The oldest student in age= 16 years. Putting in The age of the the youngest student= x-7 years The age of the middle student= x-3 years. =⇒ The age of the the youngest student= 16-7= 9 yeas. The age of the middle student= 16-3 =13 years. The age of the the youngest student= 9 yeas. The age of the middle student =13 years. Checking The oldest student in age= 16 years. 7 years younger than the oldest student=16-7=9 years. The age of the the youngest student= 9 years 4 years older than the youngest student= 4+9=13 years. The age of the middle student= 13 years. 2 The total of the ages of three students= 16+9+13=38 years. The total of the ages of three students = 38. Hence all conditions are satisfied 3