Final answer:
The sum of A, B, C, and E, which represent the coefficients of the single-scoop cones (s), double-scoop cones (d), and the constant in the total amount equation, as well as the coefficient of d in the cone count equation, is 66.
Step-by-step explanation:
The lacrosse team's coach bought a combination of single-scoop ice cream cones at $3 each and double-scoop cones at $5 each. The system of equations to represent this situation includes two equations: one for the total number of cones (s + d = 15) and one for the total amount spent on cones (3s + 5d = $57). To find the sum of A, B, C, and E, we first need to identify the coefficients and constants in our equations.
The first equation, which represents the total number of cones, has coefficients of 1 for s and 1 for d (since each cone, whether single or double-scoop, is counted as one unit). The second equation, representing the total cost, has a coefficient of 3 for s and 5 for d, and a constant of 57. If we assume A, B, and C correspond to the coefficients of s and d and the constant term in the cost equation respectively, and E corresponds to the coefficient of d in the count equation, the sum we're looking for is A + B + C + E = 3 + 5 + 57 + 1.
Therefore, the sum of A, B, C, and E is 66.