let the fixed rent be 5x and 3x
#1:
100k + 5x = 500
20k + x = 100
#2:
300k + 3x = 1100
100k + x = 1100/3
subtract them:
80k = 1100/3 - 100 = 800/3
k = 10/3
in #1 ----> 20(10/3) + x = 100
x = 100/3
So the difference is the fixed rates
= 5x-3x
= 2x
= 200/3
I was expecting the number of calls to be a whole number, but my answers do check out:
check:
calls in patna:
100(10/3) + 5(100/3) = 500
calls in bangalore:
300(10/3) + 3(100/3) = 1100
The telephone bill consists of a fixed monthly rent and a variable part that varies with the number of units of calls made per month. The monthly rents charged for a telephone connection in bangalore and patna are in the ratio 5 : 3. The bill amounts corresponding to 100 calls made from a phone in patna and 300 calls made from a phone in bangalore are respectively Rs500 and Rs1100. What is the difference in the fixed monthly rent of a telephone connection in bangalore and one in patna, if call rate per unit is same in both cities?
How to do easy way please help me
4 answers
You have made wrong equations
It will be
100k +3x = 500
300k + 5x = 1100
Which will give k = 100
And hence difference 2x = rs200
It will be
100k +3x = 500
300k + 5x = 1100
Which will give k = 100
And hence difference 2x = rs200
500
I apologize for my mistake. You are correct.
Let the fixed monthly rent for a telephone connection in Patna be 3x, and in Bangalore be 5x.
From the given information, we have:
100k + 3x = 500 ...(1)
300k + 5x = 1100 ...(2)
where k is the cost per call unit (which is the same for both cities).
Solving equation (1) for x, we get:
3x = 500 - 100k
x = (500 - 100k)/3
Substituting the value of x in equation (2), we get:
300k + 5[(500 - 100k)/3] = 1100
900k + 2500 - 500k = 3300
400k = 800
k = 2
Substituting the value of k in equation (1), we get:
100(2) + 3x = 500
3x = 300
x = 100
Therefore, the fixed monthly rent for a telephone connection in Patna is 3x = Rs. 300, and in Bangalore is 5x = Rs. 500.
The difference in the fixed monthly rent between the two cities is 5x - 3x = Rs. 200.
Let the fixed monthly rent for a telephone connection in Patna be 3x, and in Bangalore be 5x.
From the given information, we have:
100k + 3x = 500 ...(1)
300k + 5x = 1100 ...(2)
where k is the cost per call unit (which is the same for both cities).
Solving equation (1) for x, we get:
3x = 500 - 100k
x = (500 - 100k)/3
Substituting the value of x in equation (2), we get:
300k + 5[(500 - 100k)/3] = 1100
900k + 2500 - 500k = 3300
400k = 800
k = 2
Substituting the value of k in equation (1), we get:
100(2) + 3x = 500
3x = 300
x = 100
Therefore, the fixed monthly rent for a telephone connection in Patna is 3x = Rs. 300, and in Bangalore is 5x = Rs. 500.
The difference in the fixed monthly rent between the two cities is 5x - 3x = Rs. 200.