If 2x + 3y = 92 and 3x + 2y = 98, which is the larger number?
Answer and explanation
Correct answer: 22
Treat x and y as the two numbers and solve the simultaneous equations. Adding 2x + 3y = 92 and 3x + 2y = 98 gives 5x + 5y = 190, hence x + y = 38. Subtracting the first equation from the second gives x − y = 6. Adding these two simpler equations yields 2x = 44, so x = 22; consequently y = 16. Since 22 is greater than 16, the larger number is 22 and option D is correct. Option A is the smaller number. Options B and C do not satisfy the derived pair x + y = 38 together with x − y = 6, so they cannot be the requested larger value.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
Treat x and y as the two numbers and solve the simultaneous equations. Adding 2x + 3y = 92 and 3x + 2y = 98 gives 5x + 5y = 190, hence x + y = 38. Subtracting the first equation from the second gives x − y = 6. Adding these two simpler equations yields 2x = 44, so x = 22; consequently y = 16. Since 22 is greater than 16, the larger number is 22 and option D is correct. Option A is the smaller number. Options B and C do not satisfy the derived pair x + y = 38 together with x − y = 6, so they cannot be the requested larger value.
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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