The total price of one pen and one pencil is (18) rupees. The price of (2) pens and (3) pencils is (45) rupees. What is the price of one pen?
Answer and explanation
Correct answer: 9 rupees
Let the price of one pen be ₹\(x\) and that of one pencil be ₹\(y\). Then \(x+y=18\) and \(2x+3y=45\). Multiplying the first equation by 2 gives \(2x+2y=36\). Subtracting this from the second equation gives \(y=9\). Hence, \(x=18-9=9\), so one pen costs 9 rupees. If the pen cost 10 rupees, the pencil would cost 8 rupees, which does not satisfy the second condition. Exam tip: In price-based word problems, assign separate variables to the prices and form equations first.
Frequently asked questions
What is the correct answer to this question?
9 rupees
Why is this the correct answer?
Let the price of one pen be ₹\(x\) and that of one pencil be ₹\(y\). Then \(x+y=18\) and \(2x+3y=45\). Multiplying the first equation by 2 gives \(2x+2y=36\). Subtracting this from the second equation gives \(y=9\). Hence, \(x=18-9=9\), so one pen costs 9 rupees. If the pen cost 10 rupees, the pencil would cost 8 rupees, which does not satisfy the second condition. Exam tip: In price-based word problems, assign separate variables to the prices and form equations first.
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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