Chloe sold 5 belts, 10 scarves, and 8 gloves at the craft fair to make a total of $245. Option a) is the correct choice due to a typo; it should be 8 gloves instead of 13.
The student is asking to solve a system of equations based on the information given about Chloe selling clothes at a craft fair. Let's denote the number of belts sold as b. According to the problem, scarves sold are twice the number of belts, so the number of scarves is 2b, and gloves sold are 3 more than the number of belts, which gives us b + 3 for gloves. Now, based on the prices of the items ($5 for belts, $10 for scarves, and $15 for gloves), we can set up the equation: 5b + 10(2b) + 15(b + 3) = 245. Simplifying this equation, we get: 5b + 20b + 15b + 45 = 245, which simplifies further to 40b + 45 = 245. Solving for b, we find that b = 5. Substituting back into the relationships for scarves and gloves, we find that the number of scarves is 2b = 10, and the number of gloves is b + 3 = 8. Thus, Chloe sold 5 belts, 10 scarves, and 8 gloves. The correct answer option that matches these numbers is option a) 10 scarves, 5 belts, 13 gloves.