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Subjects
Class 10MathematicsPair of Linear Equations in Two VariablesAlgebraic methods: Substitution method and Elimination method.HardLevel 57
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The sum of two numbers is (52). Three times the larger number plus twice the smaller number is (136). What is the larger number?

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Answer and explanation

Correct answer: 32

Let the larger number be \(x\) and the smaller number be \(y\). Then \(x+y=52\) and \(3x+2y=136\). Multiplying the first equation by 2 gives \(2x+2y=104\). Subtracting this from the second equation gives \(x=32\). Therefore, the larger number is 32. For example, 30 does not satisfy the second condition. Exam tip: multiply one equation suitably to eliminate one variable quickly.

Related tags

Pair Of Linear EquationsElimination MethodWord ProblemsAlgebraClass 10

Frequently asked questions

What is the correct answer to this question?

32

Why is this the correct answer?

Let the larger number be \(x\) and the smaller number be \(y\). Then \(x+y=52\) and \(3x+2y=136\). Multiplying the first equation by 2 gives \(2x+2y=104\). Subtracting this from the second equation gives \(x=32\). Therefore, the larger number is 32. For example, 30 does not satisfy the second condition. Exam tip: multiply one 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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10 more MCQs
  1. 1In the equation \(2x-y=4\), what is the value of \(y\) when \(x=3\)?
  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)?
  9. 9What is the solution of the equations (x+y=5) and (x-y=1)?
  10. 10In the equations (2x+y=7) and (x=2), what is the value of (y)?
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