Let the total number of bouquets the florist arranged be $x$.

Step-by-Step Solution

1. Calculate bouquets sold in the morning:
   She sold 50% of the bouquets in the morning, so the number of bouquets sold in the morning is: $\frac{1}{2} \times x = \frac{x}{2}$

2. Calculate remaining bouquets after the morning:
   After selling half of the bouquets, she had: $x - \frac{x}{2} = \frac{x}{2}$ bouquets left.

3. Calculate bouquets sold in the afternoon:
   In the afternoon, she sold $\frac{1}{5}$ of the remaining bouquets: $\frac{1}{5} \times \frac{x}{2} = \frac{x}{10}$

4. Calculate bouquets remaining after the afternoon:
   After the afternoon sales, the number of bouquets left was: $\frac{x}{2} - \frac{x}{10} = \frac{5x - x}{10} = \frac{4x}{10} = \frac{2x}{5}$

5. Set up the equation with the given information:
   We are told she had 36 bouquets left, so: $\frac{2x}{5} = 36$

6. Solve for $x$: Multiply both sides by 5 to eliminate the fraction: $2x = 180$ Divide by 2: $x = 90$

Answer

The florist arranged 90 bouquets in total.

Would you like further details or have any questions?

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1. How would the answer change if the florist sold 60% in the morning instead of 50%?
2. What if she sold 1/4 of the remaining bouquets in the afternoon rather than 1/5?
3. How many bouquets would she have left if she sold 40% in the morning?
4. If the remaining bouquets were 50 instead of 36, what would the total be?
5. How can this type of problem be applied to inventory management in other areas?

Tip: Breaking problems into parts often helps in creating and solving equations step-by-step.