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Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.HardLevel 55
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In a class, the total number of boys and girls is (68). Twice the number of boys plus the number of girls is (112). What is the number of girls?

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Answer and explanation

Correct answer: 24

Let the numbers of boys and girls be x and y respectively. Then x+y=68 and 2x+y=112. Subtracting the first equation from the second gives x=44. Therefore, y=68-44=24. Hence, the correct answer is 24. If 26 were chosen, the total would become 70, so it cannot be correct. Exam tip: In such questions, subtracting the equations often eliminates one variable directly.

Related tags

Pair Of Linear EquationsElimination MethodWord ProblemsClass 10 MathematicsAlgebra

Frequently asked questions

What is the correct answer to this question?

24

Why is this the correct answer?

Let the numbers of boys and girls be x and y respectively. Then x+y=68 and 2x+y=112. Subtracting the first equation from the second gives x=44. Therefore, y=68-44=24. Hence, the correct answer is 24. If 26 were chosen, the total would become 70, so it cannot be correct. Exam tip: In such questions, subtracting the equations often eliminates one variable directly.

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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  2. 2Which equation is obtained by simplifying (6x+3y=12)?
  3. 3What is the point of intersection of the lines \(4x+3y=34\) and \(4x-y=10\)?
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  5. 5While solving a pair of linear equations in two variables by the elimination method, in which situation can one variable be eliminated directly?
  6. 6What is the \(x\)-coordinate of the point of intersection of the lines \(4x+5y=31\) and \(3x-2y=1\)?
  7. 7If the two lines have a unique point of intersection (r,s) that satisfies (3r+s=19) and (r-s=1), what is the value of (r+s)?
  8. 8If the unique point of intersection of two lines is (r,s) and the lines are represented by (4r+s=29) and (r-s=1), what is the value of (r+s)?
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