1. **State the problem:** We are given Jake's savings account balance as a function of weeks: $$b = 40n + 150$$ Emma's balance over weeks is given in a table: | Week (n) | 0 | 1 | 2 | 3 | 4 | 5 | |----------|---|---|---|---|---|---| | Emma's Balance | 150 | 175 | 200 | 225 | 250 | 275 | We need to find: (a) Jake's balance when Emma has $250. (b) Whose account balance is increasing at a greater rate. 2. **Find Jake's balance when Emma has $250:** From Emma's table, Emma has $250 at week $$n=4$$. Substitute $$n=4$$ into Jake's equation: $$b = 40(4) + 150$$ Calculate: $$b = 160 + 150 = 310$$ So, Jake's balance is $310 when Emma has $250. 3. **Compare the rates of increase:** - Jake's balance increases by $40 per week (coefficient of $$n$$ in Jake's equation). - Emma's balance increases by $25 per week (difference between consecutive balances: 175 - 150 = 25). Since 40 > 25, Jake's account balance is increasing at a greater rate. **Final answers:** (a) Jake's balance when Emma has $250 is $310. (b) Jake's account balance is increasing at a greater rate because $40 > 25.