Mathematics
The sum of two numbers is 43. If the larger is doubled and the smaller is tripled, the difference is 36. Find the two numbers.
Linear Equations
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Answer
Let the larger number be x and smaller number be y.
Given, sum = 43.
x + y = 43 …….(i)
According to question,
2x - 3y = 36 …….(ii)
Multiplying (i) by 3 we get,
3x + 3y = 129 ……(iii)
Adding (ii) and (iii) we get,
⇒ (2x - 3y) + (3x + 3y) = 36 + 129
⇒ 5x = 165
⇒ x = 33.
Substituting value of x in (i) we get,
⇒ 33 + y = 43
⇒ y = 43 - 33 = 10.
Hence, two numbers are 33 and 10.
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