The difference between two numbers is 8. If twice the larger number is 4 more than three times the smaller number, what is the larger number?
20
Let the larger number be \(L\) and the smaller be \(S\).
From the first condition: \(L-S=8\), so \(S=L-8\).
From the second condition: \(2L=3S+4\).
Substitute \(S=L-8\): \(2L=3(L-8)+4=3L-24+4=3L-20\).
Rearrange: \(20=3L-2L=L\), so \(L=20\).
Hence, the larger number is 20.
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