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Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.HardLevel 57
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In a class, there are (74) students. Three times the number of boys plus twice the number of girls is (186). What is the number of girls?

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Answer and explanation

Correct answer: 36

Let the number of boys be \(x\) and the number of girls be \(y\). Then \(x+y=74\) and \(3x+2y=186\). Multiplying the first equation by 2 gives \(2x+2y=148\). Subtracting this from the second equation gives \(x=38\). Hence, \(y=74-38=36\). Therefore, the correct answer is 36. Option 38 is the number of boys, not girls. Exam tip: In such questions, multiply the total-number equation suitably to eliminate one variable quickly.

Related tags

Pair Of Linear EquationsElimination MethodWord ProblemsClass 10 MathematicsNumber Of Students

Frequently asked questions

What is the correct answer to this question?

36

Why is this the correct answer?

Let the number of boys be \(x\) and the number of girls be \(y\). Then \(x+y=74\) and \(3x+2y=186\). Multiplying the first equation by 2 gives \(2x+2y=148\). Subtracting this from the second equation gives \(x=38\). Hence, \(y=74-38=36\). Therefore, the correct answer is 36. Option 38 is the number of boys, not girls. Exam tip: In such questions, multiply the total-number equation suitably to eliminate one variable quickly.

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 \(4x-y=10\)?
  4. 4If the lines \(x+y=9\) and \(kx+3y=23\) both pass through the point \(\left(4,5\right)\), what is the value of \(k\)?
  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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