Three pens and two notebooks cost 86 rupees. Two pens and three notebooks cost 89 rupees. What is the price of one pen?
Answer and explanation
Correct answer: 16 rupees
Let p be the price of one pen and n be the price of one notebook. The statements form the simultaneous equations 3p + 2n = 86 and 2p + 3n = 89. Multiply the first equation by 3 and the second by 2: 9p + 6n = 258 and 4p + 6n = 178. Subtracting eliminates n and gives 5p = 80, so p = 16. Substitution gives 2(16) + 3n = 89, hence n = 19, which checks in the first equation: 3(16) + 2(19) = 86. Therefore one pen costs 16 rupees, so option A is correct; the other choices confuse the notebook price or arise from an elimination error.
Frequently asked questions
What is the correct answer to this question?
16 rupees
Why is this the correct answer?
Let p be the price of one pen and n be the price of one notebook. The statements form the simultaneous equations 3p + 2n = 86 and 2p + 3n = 89. Multiply the first equation by 3 and the second by 2: 9p + 6n = 258 and 4p + 6n = 178. Subtracting eliminates n and gives 5p = 80, so p = 16. Substitution gives 2(16) + 3n = 89, hence n = 19, which checks in the first equation: 3(16) + 2(19) = 86. Therefore one pen costs 16 rupees, so option A is correct; the other choices confuse the notebook price or arise from an elimination error.
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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