1.a bus is carrying 40 passengers some with 25 rupees ticket and the remaining with 30 rupees ticket. if the total amount collected from these passengers is 1125 rupees. find the number of passengers who have taken 25 rupees ticket
2.divide AED 1380 among Ahmed John and Babita so that the amount Ahmed receives is 5 times as much as babita's share and its 3 times as much as John's share
thank you REINY
To solve these questions, we can use a system of equations.
1. Let's assume the number of passengers with a 25 rupees ticket is 'x'. Then, the number of passengers with a 30 rupees ticket would be '40 - x'.
The amount collected from passengers with a 25 rupees ticket would be 25x rupees, and the amount collected from passengers with a 30 rupees ticket would be 30(40 - x) rupees.
According to the given information, the total amount collected is 1125 rupees. Therefore, we can form the equation:
25x + 30(40 - x) = 1125.
To solve the equation, we can simplify it:
25x + 1200 - 30x = 1125,
-5x = -75,
x = 15.
So, the number of passengers who have taken a 25 rupees ticket is 15.
2. Let's assume Babita's share is 'x' AED. Then, Ahmed's share would be 5 times Babita's share, which is 5x AED. John's share would be 1/3 of Ahmed's share, which is (1/3)(5x) = (5/3)x AED.
According to the given information, the total amount divided is 1380 AED. Therefore, we can form the equation:
x + 5x + (5/3)x = 1380.
To solve the equation, we can simplify it:
(1 + 5 + 5/3)x = 1380,
(15/3 + 25/3 + 5/3)x = 1380,
(45/3)x = 1380,
(15/1)x = 1380,
15x = 1380,
x = 92.
So, Babita's share is 92 AED, Ahmed's share is 5x92 = 460 AED, and John's share is (5/3)x92 = 230 AED.
number of 25 rupees tickets ---x
number of 30 rupees tickets --- 40-x
25x + 30(40-x) = 1125
solve for x
#2
John ---x
Babita -- 3x
Ahmed ---5(3x) = 15x
so ......
Answer 1:
x + y = 40 (X by -25 for elimination)
25x + 30y = 1125
-25x - 25y = -1000
25x + 30y = 1125
___________________
5y = 125
y = 25 (plug in for y to find x)
x + 25 = 40
x = 40 - 25
x = 15
total number of passengers that bought 25 rupees ticket = 15