Every "share an amount in a ratio" question runs on the same four moves. Learn them once and you never have to think about it again.
The Four Moves
One — add the parts. The ratio a : b has a + b equal parts in total. That sum is the number you'll divide by.
Two — find one part. one part = whole ÷ total parts. This is the heart of it — the value of a single equal chunk.
Three — scale each share. Each person's share is their parts × value of one part. So one gets a × (one part), the other gets b × (one part).
Four — check it adds back. The two shares must total the whole again. If they don't, hunt for the slip.
A Worked One
Share $30 in the ratio 3 : 2. Parts: 3 + 2 = 5. One part: 30 ÷ 5 = 6. Shares: 3 × 6 = 18 and 2 × 6 = 12. Check: 18 + 12 = 30 ✓. Done — $18 and $12.
Three-part Ratios? Same Deal
If the ratio is 2 : 3 : 5, nothing changes — there are just more parts. Total parts = 2 + 3 + 5 = 10, find one part, then scale all three. The method doesn't care how many people are sharing.