1. **State the problem:** Ricky initially had 3 times as much money as Lina. After both spent 180, Ricky had 5 times as much money as Lina. We need to find how much money each had at first. 2. **Define variables:** Let Lina's initial amount be $L$. Then Ricky's initial amount is $3L$. 3. **Write the equations after spending:** After spending 180 each, Lina has $L - 180$ and Ricky has $3L - 180$. 4. **Use the given ratio after spending:** Ricky's remaining money is 5 times Lina's remaining money: $$3L - 180 = 5(L - 180)$$ 5. **Expand and simplify:** $$3L - 180 = 5L - 900$$ 6. **Rearrange terms:** $$3L - 180 - 5L + 900 = 0$$ $$-2L + 720 = 0$$ 7. **Solve for $L$:** $$-2L + 720 = 0$$ $$-2L = -720$$ $$L = \frac{\cancel{-720}}{\cancel{-2}} = 360$$ 8. **Find Ricky's initial amount:** $$3L = 3 \times 360 = 1080$$ 9. **Final answer:** Lina had 360 initially, Ricky had 1080 initially.