Mathematics
The sum of two numbers exceeds thrice the smaller by 2. If the difference between them is 19, find the numbers.
Linear Equations
3 Likes
Answer
Let the numbers be x and y, such that x < y.
Given,
The sum of two numbers exceeds thrice the smaller by 2.
∴ (x + y) - 3x = 2
⇒ x - 3x + y = 2
⇒ y - 2x = 2 ……(1)
Given,
Difference between the numbers = 19
⇒ y - x = 19 ……(2)
Subtracting equation (1) from (2), we get:
⇒ y - x - (y - 2x) = 19 - 2
⇒ y - x - y + 2x = 19 - 2
⇒ x = 17.
Substituting value of x in equation (1), we get :
⇒ y - 2x = 2
⇒ y - 2 × 17 = 2
⇒ y - 34 = 2
⇒ y = 36.
Hence, the numbers are 17 and 36.
Answered By
2 Likes
Related Questions
Solve the following system of equations by using the method of cross multiplication:
, where x ≠ -1 and x ≠ 1.
The sum of two numbers is 53 and their difference is 25. Find the numbers.
The sum of two numbers is 51. If the larger is doubled and the smaller is tripled, the difference is 12. Find the numbers.
Find two numbers such that the sum of twice the first and thrice the second is 103 and four times the first exceeds seven times the second by 11.