1. **State the problem:** Barbara orders twice as many hot dogs as pieces of cake for a group of girls. A hot dog costs 5 and a piece of cake costs 2. The total cost is 60. Each girl receives either a hot dog or a piece of cake. We need to find how many girls are in the group. 2. **Define variables:** Let $c$ be the number of pieces of cake. Then the number of hot dogs is $2c$ because Barbara orders twice as many hot dogs as pieces of cake. 3. **Write the cost equation:** The total cost is the sum of the cost of hot dogs and cakes: $$5 \times (2c) + 2 \times c = 60$$ 4. **Simplify the equation:** $$10c + 2c = 60$$ $$12c = 60$$ 5. **Solve for $c$:** $$c = \frac{60}{12}$$ $$c = 5$$ 6. **Find the number of hot dogs:** $$2c = 2 \times 5 = 10$$ 7. **Find the total number of girls:** Each girl receives either a hot dog or a piece of cake, so total girls = number of hot dogs + number of cakes: $$10 + 5 = 15$$ **Final answer:** There are **15** girls in the group.