Final answer:
By setting up algebraic expressions to represent the number of free throws made by each person and solving the resulting equation, we can determine that Sean made 9 free throws, Emilie made 3, and Alison made 5.
Step-by-step explanation:
Let's represent the number of free throws Emilie made as E. Since Sean made 6 more than Emilie, we can say Sean made E + 6 free throws. Emilie made 2 less than Alison, so if we let A represent the number of free throws Alison made, Emilie made A - 2 free throws. We know that Emilie's free throws E are the same as A - 2, so E = A - 2. The total number of free throws made by all three is 17, so the equation is E + (E + 6) + A = 17.
Substitute A - 2 for E in the equation: (A - 2) + ((A - 2) + 6) + A = 17. Simplified, this becomes 3A + 2 = 17. Solving for A, we find that Alison made 5 free throws. This means Emilie made 3 free throws (A - 2), and Sean made 9 free throws (E + 6).