Rs 10
5 notes
Rs 5
7 notes
Total number of notes =
12
Total Amount =
10 x 5
+
5 x 7
= Rs. 85
Meena went to a bank to withdraw Rs. 2000. She asked the cashier to give her Rs. 50 and
Rs. 100 notes only.
Meena got 25 notes in all.
Find how many notes of Rs. 50 and Rs. 100 she received.
(iv)
Sol.
| | | |
| | | |
| | | |
Rs. 50
Rs. 100
Total
No. of notes
x
y
Amount
50 x
100 y
2000
As per the 1st given condition,
50 x
+
100 y
= 2000
Dividing throughout by 50, we get
x
+
2y
= 40
........(i)
As per the 2nd given condition,
x
+
y
= 25
........(ii)
25
Let us learn this sum with the help of table
Total Amount = Rs. 2000
Solve the equations by either Substitution or Elimination Method
y = 15
x
=
Substituting y = 15 in (ii)
10
∴ Meena will receive 10 notes of Rs. 50 and 15 notes of RS. 100
A part of monthly hostel charges is fixed and the remaining part depends on the
number of days one has taken food in the mess.
When a student A takes food for 20 days she pays Rs. 1000 as hostel charges
Whereas a student B takes food for 26 days and pays Rs. 1180 as hostel charges.
Find the fixed charge and the cost of food per day.
Q)
Sol.
As per the 1st given condition,
x
+
20
y
= 1000
As per the 2nd given condition,
x
+
26
= 1180
y
........(ii)
.......(i)
Let the fixed charge be Rs. x and the cost of food per day be Rs. y
What we need to find?
Lets understand this sum with an example
Fixed charge
Rs. 100
Cost of food per day
Rs. 50
Cost for 1 day =
100
+
1 x 50
Cost for 2 days =
100
+
2 x 50
Cost for 3 days =
100
+
3 x 50
What do we observe?
Irrespective of number of days…
Fixed charge remain the same
Cost of food changes as per the number of days
Total Cost = fixed charge + no. of days x cost of food per day
Solve the equations with either substitution or elimination method
y
= 30
Substituting y = 30 in (i)
x
= 400
Fixed Charge is Rs. 400 and cost of food per day is Rs. 30
Total Cost = x + no. of days x y
A lending library has a fixed charge for first 3 days and an additional charge for each day thereafter.
Saritha paid Rs. 27 for the book kept for 7 days
While Susy paid Rs. 21 for the book she kept for 5 days
Find the fixed charge and the charge for each extra day
Q)
Sol.
As per the 1st given condition,
x
+
4
y
= 27
As per the 2nd given condition,
x
+
2
= 21
y
........(ii)
.......(i)
Let the fixed charge be Rs. x and the charge for each extra day be Rs. y
What we need to find?
What is the difference between this sum and previous sum?
In this sum, additional charge is collected only after 3 days
Hence additional charge will be collected only for
7 – 3 = 4 days
In the first condition
Total Number of days = 7
Solve the equations with either substitution or elimination method
y
= 3
Substituting y = 3 in (i)
x
= 15
Fixed Charge is Rs. 15 and Charge for extra day is Rs. 3
In the Second condition
Total Number of days = 5
Hence additional charge will be collected only for
5 – 3 = 2 days