Problem 1 :
The sum of three consecutive multiples of 8 is 888. Find the multiples.
Problem 2 :
The ages of John and David are in the ratio 5 : 7. Four years later the sum of their ages will be 56 years. What are their present ages ?
Problem 3 :
The number of boys and girls in a class are in the ratio 7 : 5. The number of boys is 8 more than the number of girls. What is the total class strength ?
Problem 4 :
Baichung's father is 26 years younger than Baichung's grandfather and 29 years older than Baichung. The sum of the ages of all the three is 135 years. What is the age of each one of them?
Problem 5 :
The organizers of an essay competition decide that a winner in the competition gets a prize of $100 and a participant who does not win gets a prize of $25. The total prize money distributed is $3000. Find the number of winners, if the total number of participants is 63.
1. Answer :
Let the three consecutive multiples of 8 be
x, (x + 8) and (x + 16)
Given : The sum of three consecutive multiples of 8 is 888.
Then, we have
x + (x + 8) + (x + 16) = 888
3x + 24 = 888
Subtract 24 from each side.
3x = 864
Divide each side by 24.
x = 288
Then,
x + 8 = 288 + 8 = 296
x + 16 = 288 + 16 = 304
So, the three consecutive multiples of 8 are 288, 296, and 304.
2. Answer :
Given : The ages of John and David are in the ratio 5 : 7.
Then, the present ages of John and David are
5x and 7x
Given : Four years later the sum of their ages will be 56 years.
Then, we have
(5x + 4) + (7x + 4) = 56
Simplify and solve for x.
12x + 8 = 56
Subtract 8 from each side.
12x = 48
Divide each side by 12.
x = 4
Age of John is
5x = 5(4)
5x = 20
Age of David is
7x = 7(4)
7x = 28
So, the present ages of John and David are 20 years and 28 years respectively.
3. Answer :
Given : The number of boys and girls in a class are in the ratio 7 : 5.
Then,
Number of boys = 7x
Number of girls = 5x
Given : The number of boys is 8 more than the number of girls.
Then, we have
7x = 5x + 8
Subtract 5x from each side.
2x = 8
Divide each side by 2.
x = 4
Number of boys is
7x = 7(4)
7x = 28
Number of girls is
5x = 5(4)
5x = 20
Total number of students in the class is
= 28 + 20
= 48
So, the total class strength is 48.
4. Answer :
Let x be the age Baichung's father.
Then,
Age of Baichung = x - 29
Age of Baichung's grandfather = x + 26
Given : The sum of the ages of all the three is 135 years.
Then, we have
x + (x - 29) + (x + 26) = 135
3x - 3 = 135
Add 3 to each side.
3x = 138
Divide each side by 3.
x = 46
Age of Baichung's father is is 46 years.
x - 29 = 46 - 29
x - 29 = 17
Age of Baichung is 20 years.
x + 26 = 46 + 26
x + 26 = 72
Age of Baichung's grand father is 72 years.
5. Answer :
Let x be the number of winners.
Then, the number of participants do not win is (63 - x).
Given : Winner gets $100, loser gets $25 and total prize money distributed is $3000.
Then, we have
100x + 25(63 - x) = 3000
100x + 1575 - 25x = 3000
75x + 1575 = 3000
75x = 1425
Divide each side by 75.
x = 19
So, the number of winners is 19.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Sep 29, 22 04:11 AM
Sep 29, 22 04:08 AM
Sep 29, 22 12:02 AM