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Question
Two numbers differ by 3. The sum of twice the smaller number and thrice the greater number is 19. Find the numbers.
Solution
Let the greater number be x and the smaller number be y.
By first condition:
Two numbers differ by 3.
x − y = 3 ...(1)
By second condition:
The sum of twice the smaller number and thrice the greater number is 19.
2y → Twice the smaller number + 3x → Thrice the greater number = 19
2y + 3x = 19
3x + 2y = 19 ...(2)
Multiplying equation (1) by 2
2x − 2y = 6 ...(3)
Adding equations (2) and (3)
3x + 2y = 19
2x − 2y = 6
5x = 25
x = `25/5`
x = `5`
Put x = 5 in equation (1)
x − y = 3
5 − y = 3
5 − 3 = y
2 = y
y = 2
∴ The numbers are 5 and 2.
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