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

2024
Views:

454

Pages:

6
Author:

Shahbaz A.

Algebra words Problems shahbaz ahmed July 2024 Algebra Word Problems Packet No 1 Q 1. Twice a number is 500 more than six times the number. What is the number? Solution Let number=x Twice of number =2x 500 more than twice the number=2x+500 six times the number=6x According to the condition 6x = 2x + 500 6x − 2x = 2x + 500 − 2x 1 6x − 2x = 2x + 500 − 2x 4x = 500 x= 500 4 x = 125 x=125 Checking Number=125 Twice of number =2(125)=250 500 more than twice the number=250+500=750 six times the number=6(125)=750 Hence six times the number=500 more than twice the number ......................................................... Q2. Three-sevenths of a number is 24. Find the number Solution Let number=x Three-sevenths of the number= 37 x According to the condition 3 7x = 24 2 3x = 24 × 7 x= 24×7 3 x=8×7 x=56 Checking Three-sevenths of the number= 37 × 56= 24 ......................................................................... Q3 What number increased by ¼ of itself is equal to 30 Solution Let number=x ¼ of itself= 14 x Number increased by ¼ of itself=x + 41 x According to the condition x + 14 x = 30 (1 + 14 )x = 30 5 4x = 30 4 × 54 x = 4 × 30 5x = 120 x= 120 5 = 24 3 x=24 Checking ¼ of 24= 14 (24) = 6 24 increased by ¼ of 24=24 + 6 = 30 ............................................................................ Q 4. Find a number such that ¼ of the number is 50 less than 2 3 of the number Solution Let number=x 1 4 of the number= 41 x 2 3 of number= 32 x 50 less than 2 3 of the number= 32 x − 50 According to the condition 1 4x = 32 x − 50 Multiplying by 12 12 × 14 x = 12 × 23 x − 12 × 50 3x = 8x − 600 Or 8x − 600 = 3x 4 8x − 600 + 600 = 3x + 600 8x = 3x + 600 8x − 3x = 3x + 600 − 3x 5x = 600 x= 600 5 = 120 x=120 checking Number =120 1 4 of the 120= 2 3 of 120= 2 3 50 less than 1 4 × 120 = 30 × 120 = 80 2 3 of the 120= 80 − 50 = 30 Hence 1 4 of the 120=50 less than 2 3 of the 120=30 ........................................................................... Q5. The denominator of a fraction exceeds the numerator of a fraction by 25. The value of the fraction is 38 .Find the fraction. Solution Let numerator=x 5 denominator= 25 exceeded by numerator= x+25 According to the condition x x+25 = 3 8 8x = 3(x + 25) 8x = 3x + 75 8x − 3x = 3x + 75 − 3x 5x = 75 x= 75 5 x = 15 Let numerator=15 denominator= 25 exceeded by numerator= 15+25=40 x x+25 x x+25 = = 15 40 15 40 Checking x x+25 = 15 40 = 3×5 8×5 = 3 8 ....................................................................... 6