Three pencils and two erasers cost (31) rupees. Two pencils and five erasers cost (47) rupees. What is the price of one pencil?
Answer and explanation
Correct answer: (61/11) rupees
Let the price of one pencil be \(p\) rupees and that of one eraser be \(e\) rupees. The equations are \(3p+2e=31\) and \(2p+5e=47\). Multiplying the first equation by 5 and the second by 2 gives \(15p+10e=155\) and \(4p+10e=94\). Subtracting, \(11p=61\), so \(p=\frac{61}{11}\) rupees. Therefore, option B is correct. The value 6 rupees in option C is close, but it does not satisfy the equations exactly. Exam tip: In the elimination method, make the coefficients of one variable equal before adding or subtracting the equations.
Frequently asked questions
What is the correct answer to this question?
(61/11) rupees
Why is this the correct answer?
Let the price of one pencil be \(p\) rupees and that of one eraser be \(e\) rupees. The equations are \(3p+2e=31\) and \(2p+5e=47\). Multiplying the first equation by 5 and the second by 2 gives \(15p+10e=155\) and \(4p+10e=94\). Subtracting, \(11p=61\), so \(p=\frac{61}{11}\) rupees. Therefore, option B is correct. The value 6 rupees in option C is close, but it does not satisfy the equations exactly. Exam tip: In the elimination method, make the coefficients of one variable equal before adding or subtracting the equations.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..
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