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

2023
Views:

323

Pages:

2
Author:

Shahbaz A.

Q64 Algebra Word Problems Packet No 1 shahbaz ahmed August 2024 Q 64.In five years the sum of Don’s and Dan’s ages will be 34. Don’s age now is 8 years less than three times Dan’s age. How old is Don? Solution Let Dan’s age.= x years. Three times Dan’s age.=3x years. 8 years less than three times Dan’s age=3x-8 years =⇒ Don’s age= 3x-8 years In 5 years , Dan’s age.= x+5 years. in 5 years, Don’s age= 3x-8+5=3x-3 years In 5 years , sum of Dan’s age and Don’s age=x+5+3x-3=4x+2 years. In 5 years , sum of Dan’s age and Don’s age=34 years. According to the condition 1 4x + 2 = 34 4x + 2 − 2 = 34 − 2 4x = 32 x= 32 4 x = 8 years. Dan’s age.= 8 years. Putting in Don’s age= 3x-8 years Don’s age= 3(8)-8=16 years Checking Dan’s age.= 8 years. Three times Dan’s age.=3(8)=24 years. 8 years less than three times Dan’s age=24-8=16 years =⇒ Don’s age= 16 years In 5 years , Dan’s age.= 8+5=13 years. in 5 years, Don’s age= 16+5=21 years In 5 years , sum of Dan’s age and Don’s age=13+ 21= 34 years. In 5 years , sum of Dan’s age and Don’s age=34 years. All conditions are satisfied 2