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Q2(v):
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (v) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ` 27 for a book kept for seven days, while Susy paid ` 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Solution :
Given:
A lending library charges a fixed amount for the first three days and an additional charge for each day thereafter. Saritha paid ₹27 for a book kept for 7 days. Susy paid ₹21 for a book kept for 5 days.
To Find:
The fixed charge for the first three days and the additional charge for each extra day.
Step 1: Defining Variables
Let the fixed charge for the first three days be $x$ (in ₹).
Let the additional charge for each extra day be $y$ (in ₹).
Step 2: Formulating the Equations
For Saritha: She kept the book for 7 days. This includes 3 fixed days and 4 extra days ($7 - 3 = 4$).
The equation is: $x + 4y = 27$ --- (Equation 1)
For Susy: She kept the book for 5 days. This includes 3 fixed days and 2 extra days ($5 - 3 = 2$).
The equation is: $x + 2y = 21$ --- (Equation 2)
Step 3: Solving by Elimination Method
To eliminate $x$, we subtract Equation 2 from Equation 1:
$(x + 4y) - (x + 2y) = 27 - 21$
$x - x + 4y - 2y = 6$
$2y = 6$
$y = \frac{6}{2}$
$y = 3$
[Since the additional charge per day is ₹3]
Step 4: Finding the value of $x$
Substitute the value of $y = 3$ into Equation 2:
$x + 2(3) = 21$
$x + 6 = 21$
$x = 21 - 6$
$x = 15$
[Since the fixed charge for the first three days is ₹15]
Step 5: Verification
Check with Equation 1: $15 + 4(3) = 15 + 12 = 27$. (Matches the given condition for Saritha).
Final Answer: The fixed charge for the first three days is ₹15 and the charge for each extra day is ₹3.
More Questions from Class 10 Mathematics Pair of linear equations in two variable EXERCISE 3.3
- Q1(i): Solve the following pair of linear equations by the elimination method and the substitution method : (i) x + y = 5 and 2x – 3y = 4
- Q1(ii): Solve the following pair of linear equations by the elimination method and the substitution method : (ii) 3x + 4y = 10 and 2x – 2y = 2
- Q1(iii): Solve the following pair of linear equations by the elimination method and the substitution method : (iii) 3x – 5y – 4 = 0 and 9x = 2y + 7
- Q1(iv): Solve the following pair of linear equations by the elimination method and the substitution method : (iv) $\frac{x}{2} + \frac{2y}{3} = -1$ and $x - \frac{y}{3} = 3$
- Q2(i): Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (i) If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes $\frac{1}{2}$ if we only add 1 to the denominator. What is the fraction?
- Q2(ii): Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (ii) Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
- Q2(iii): Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (iii) The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
- Q2(iv): Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method : (iv) Meena went to a bank to withdraw ` 2000. She asked the cashier to give her ` 50 and ` 100 notes only. Meena got 25 notes in all. Find how many notes of ` 50 and ` 100 she received.
CBSE Solutions for Class 10 Mathematics Pair of linear equations in two variable
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