The sum of two numbers is 51. If the larger is doubled and the smaller is tripled, the difference is 12. Find the numbers.
Linear Equations
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Question

The sum of two numbers is 51. If the larger is doubled and the smaller is tripled, the difference is 12. Find the numbers.

KnowledgeBoat · Accepted Answer

Let two numbers be x and y, where x y. Given, Sum of numbers = 51 ⇒ x + y = 51 ⇒ x = 51 - y ......(1) Given, Difference of numbers when larger is doubled and the smaller is tripled = 12 ⇒ 2x - 3y = 12 ......(2) Substituting value of x from equation (1) in (2), we get : ⇒ 2(51 - y) - 3y = 12 ⇒ 102 - 2y - 3y = 12 ⇒ -5y = 12 - 102 ⇒ -5y = -90 ⇒ y = . Substituting value of y in equation (1), we get : ⇒ x = 51 - y ⇒ x = 51 - 18 ⇒ x = 33. Hence, the numbers are 33 and 18.

Mathematics

The sum of two numbers is 51. If the larger is doubled and the smaller is tripled, the difference is 12. Find the numbers.

Linear Equations

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