If twice the smaller of two numbers is added to three times the larger number, the result is 55. If the larger is increased by 5, it becomes twice the smaller. What is the larger number?
12.5
Let the smaller number be x and the larger be y. From the first condition: \(2x+3y=55\).
From the second condition: \(y+5=2x \Rightarrow x=\dfrac{y+5}{2}\).
Substituting: \(2\times\dfrac{y+5}{2}+3y=55 \Rightarrow (y+5)+3y=55 \Rightarrow 4y=50 \Rightarrow y=12.5\).
Hence, the larger number is 12.5.
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Important Questions from Linear Equation in 2 Variable
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