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

2023
Views:

233

Pages:

4
Author:

Shahbaz A.

words problems Q12,Q13,Q14 shahbaz ahmed July 2024 Q 12.The second of three numbers is one less than the first. The third number is 5 less than twice the second. If the third number exceeds the first number by 12, find the three numbers. Solution Let first number=x One less than the first=x-1 =⇒ second=x-1 Twice the second=2(x-1) 5 less than twice the second=2(x-1)-5 Third number=2(x-1)-5 According to the condition. Third number -First number=12 2(x − 1) − 5 − x = 12 2x − 2 − 5 − x = 12 1 2x − x − 7 = 12 x − 7 = 12 x − 7 + 7 = 12 + 7 x = 19 First Number=19 Second Number=19-1=18 Third Number=2(19-1)-5=31 Q 13.One number is 4 more than 5 times another number. If 6 is added to each, the first resulting number is three times the second resulting number. Find the two numbers. Solution Let another number(Second Number)=x 5 times second number=5x 4 more than 5 times second number=5x+4 One number(first number)=5x+4 6 is added to first number=5x+4+6=5x+10 6 is added to second number=x+6 According to the condition. 5x + 10 = 3(x + 6) 5x + 10 = 3x + 18 5x + 10 − 10 = 3x + 18 − 10 5x = 3x + 8 2 5x − 3x = 3x + 8 − 3x 2x = 8 x= 8 2 =4 Second Number=4 First Number=5(4)+4=24 CHECKING 6 added to the first= 24+6=30 6 added to the second= 4+6=10 According to the condition 30 = 3× 10 30=30 Condition is satisfied Q 14.When you started your homework assignment, your friend already had 6 exercises done. You can do about 3 exercises per minute, whereas your friend can only do 2 exercises per minute. How many minutes will it take you to catch up to your friend. solution Let number of minutes work is done=x minutes Number of exercises done by me=3x Number of exercises done by my friend=2x According to the condition 3x = 2x + 6 3x − 2x = 2x + 6 − 2x x=6 3 Number of minutes required to catch up friend=6 minutes CHECKING Number of exercises done by me in 6 minutes =6 ×3 =18 Number of exercises done by my friend in 6 minutes = 6 × 2=12 6 added to Number of exercises done by my friend in 6 minutes=12+6=18 Hence given condition is satisfied 4