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

2024
Views:

431

Pages:

4
Author:

Shahbaz A.

words problems shahbaz ahmed July 2024 Q7. If 3 times a number is increased by 22, the result is 14 less than 7 times the number. What is the number? Solution Let number=x 3 times a number =3x 3 times a number is increased by 22=3x+22 7 times the number=7x 14 less than 7 times the number=7x-14 According to the condition 7x − 14 = 3x + 22 7x − 14 + 14 = 3x + 22 + 14 7x = 3x + 36 7x − 3x = 3x + 36 − 3x 4x = 36 x = 36 4 = 9 Number=9 Checking Putting x=9 in: 7x − 14 = 3x + 22 7 × 9 − 14 = 3 × 9 + 22 63 − 14 = 27 + 22 49 = 49 1 .............................................................. Q8. Separate 84 into two parts such that one part will be 12 less than twice the other. Solution Let one part=x Other part=84-x Twice the other=2(84-x) 12 less than twice the other=2(84-x)-12 According to the condition x = 2(84 − x) − 12 x = 168 − 2x − 12 x = 156 − 2x x + 2x = 156 − 2x + 2x 3x = 156 x = 156 3 x = 52 Since Other part=84-x =⇒ Other part=84-52=32 One part =52, Other part=32 Checking Putting x=52 in: 52 = 2(84 − 52) − 12 52 = 2(32) − 12 52 = 64 − 12 52 = 52 L.H.S=R.H.S ................................................................... Q9. The difference between two numbers is 24. Find the numbers if their sum is 88. Solution Let one number=x 2 Other number=y According to the conditions Difference=x − y = 24 ........... eq(1) Sum=x + y = 88 ....................eq (2) Adding eq(1) and eq(2) x − y + x + y = 24 + 88 2x = 112 x = 112 2 x = 56 Putting in equation (1) 56-y=24 −y = 24 − 56 −y = −32 y = 32 One number=56, Other number 32 Checking Difference=x − y = 56 − 32 = 24 Sum=x + y = 56 + 32 = 88 ................................................................. Q 10.One number is 3 times another number. If 17 is added to each, the first resulting number is twice the second resulting number. Find the two numbers. Solution Let another number=y 3 times another number=3y One number= 3 times another number=3y 17 is added to another number=y+17 3 17 added to one number=3y+17 According to the condition 3y + 17 = 2(y + 17) 3y + 17 = 2y + 34 3y + 17 − 17 = 2y + 34 − 17 3y = 2y + 17 3y − 2y = 2y + 17 − 2y y = 17 Another number=17 One number=3y Or One number=3 × 17 = 51 First number=51 , Second number=17 4