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

2023
Views:

373

Pages:

3
Author:

Shahbaz A.

Q 60 Algebra Word Problems Packet No 1 shahbaz ahmed August 2024 Q 60.Mattie is twice as old as Pat. Jon is twice as old as Mattie. In 4 years the sum of their ages will be 61. How old is each person? Solution Let age of Pat=x years. Twice as old as Pat.=2x years. Age of Mattie =2x years. Twice of Mattie =4x years. Age of Jon=4x years. In 4 years, let age of Pat=x+4 years. In 4 years, age of Mattie =2x+4 years. in 4 years, Age of Jon= 4x+4 years. 1 In 4 years ,sum of ages=x+4+2x+4+4x+4=7x+12 years. In 4 years, given sum of ages=61 years. According to the condition. 7x + 12 = 61 7x + 12 − 12 = 61 − 12 7x = 49 x= 49 7 x = 7 years. Age of Pat=7 years. Putting in Age of Mattie =2x years. Age of Jon=4x years. =⇒ Age of Mattie =2×7=14 years. Age of Jon=4× 7=28 years. Age of Mattie =14 years. Age of Jon=28 years. Checking Age of Pat=7 years. 2 Twice as old as Pat.=2×7=14 years. Age of Mattie =14 years. Twice of Mattie =2 ×14=28 years. Age of Jon=28 years. In 4 years, let age of Pat=7+4=11 years. In 4 years, age of Mattie =2(7)+4=18 years. in 4 years, Age of Jon= 4(7)+4=32 years. In 4 years ,sum of ages=11+18+32=61 years. In 4 years, given sum of ages=61 years. All conditions are satisfied 3