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Question
The difference of two numbers is 3, and the sum of three times the larger one and twice the smaller one is 19. Find the two numbers.
Solution
Let the larger number be x and the smaller number be y.
According to given information, we have
x - y = 3
⇒ x - 3 + y ....(i)
Also, 3x + 2y = 19
⇒ 3(3 + y) + 2y = 19 ....[From (i)]
⇒ 9 + 3y + 2y = 19
⇒ 5y = 10
⇒ y = 2
⇒ x = 3 + 2
= 5
Thus, the required numbers are 5 and 2 respectively.
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