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Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.MediumLevel 55
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A pen costs p and a notebook costs q. If 3p + 4q = 260 and 5p + 2q = 300, what is q?

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Answer and explanation

Correct answer: 200/7

This is a pair of linear equations representing two prices. To eliminate q, multiply 5p + 2q = 300 by 2, obtaining 10p + 4q = 600. Subtract 3p + 4q = 260 from it: 7p = 340, so p = 340/7. Substitute this into 5p + 2q = 300: 5(340/7) + 2q = 300. Thus 1700/7 + 2q = 2100/7, giving 2q = 400/7 and q = 200/7. Therefore option C is correct. The other values would make the two original price equations inconsistent, so they cannot represent the notebook price in this system.

Related tags

Pair-Of-Linear-EquationsWord-ProblemEliminationAlgebraic Methods: Substitution Method And Elimination Method.Algebraic Methods Substitution Method And Elimination MethodPair Of Linear Equations In Two VariablesMathematicsClass 10 Mcq

Frequently asked questions

What is the correct answer to this question?

200/7

Why is this the correct answer?

This is a pair of linear equations representing two prices. To eliminate q, multiply 5p + 2q = 300 by 2, obtaining 10p + 4q = 600. Subtract 3p + 4q = 260 from it: 7p = 340, so p = 340/7. Substitute this into 5p + 2q = 300: 5(340/7) + 2q = 300. Thus 1700/7 + 2q = 2100/7, giving 2q = 400/7 and q = 200/7. Therefore option C is correct. The other values would make the two original price equations inconsistent, so they cannot represent the notebook price in this system.

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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