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Question
Find the numbers such that the sum of thrice the first and the second is 142, and four times the first exceeds the second by 138.
Solution
Let the first number be x and the second number be y.
Then, we have:
3x + y = 142 ……….(i)
4x - y = 138 ………(ii)
On adding (i) and (ii), we get
7x = 280
⇒ x = 40
On substituting x = 40 in (i), we get:
3 × 40 + y = 142
⇒ y = (142 – 120) = 22
⇒ y = 22
Hence, the first number is 40 and the second number is 22.
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