1. **State the problem:** A baker made 3 kinds of bagels: plain, cheese, and sesame seed. Three-eighths of the bagels were plain, one-fifth were cheese, and the rest were sesame seed. There were 28 fewer cheese bagels than plain bagels. We need to find how many sesame seed bagels there were. 2. **Define variables:** Let the total number of bagels be $x$. 3. **Express quantities:** - Plain bagels = $\frac{3}{8}x$ - Cheese bagels = $\frac{1}{5}x$ - Sesame seed bagels = $x - \left(\frac{3}{8}x + \frac{1}{5}x\right)$ 4. **Use the given difference:** Cheese bagels are 28 fewer than plain bagels: $$\frac{3}{8}x - \frac{1}{5}x = 28$$ 5. **Find common denominator and simplify:** $$\frac{15}{40}x - \frac{8}{40}x = 28$$ $$\frac{7}{40}x = 28$$ 6. **Solve for $x$:** $$x = 28 \times \frac{40}{7}$$ $$x = 28 \times \cancel{\frac{40}{7}}$$ $$x = 28 \times \frac{40}{7} = 4 \times 40 = 160$$ 7. **Calculate sesame seed bagels:** $$\text{Sesame} = 160 - \left(\frac{3}{8} \times 160 + \frac{1}{5} \times 160\right)$$ $$= 160 - (60 + 32)$$ $$= 160 - 92 = 68$$ **Final answer:** There were 68 sesame seed bagels.