Lizzy: Paul's grades last semester were very bad. To encourage him, Paul's dad promised him $5 for every B+ he gets in his next scorecard and twice that amount for every A. If Paul obtains at least two A+ he'll double the previous rewards and would receive a flat $15 for every A+ obtained (with no extra bonus). If there are 10 courses with grades in Paul's scorecard, what's the maximum amount he could receive from his dad?.
Me: Hmmm, let me think. I think this is the detailed solution:
We know Paul would get $5 for a B + . However, we know this could be (2x) doubled if he obtains at least two A + . This means 2 * $5 = $10 for a B + if Paul gets at least two A + . We know Paul would get twice the reward of a B + if he gets an A. This means 2 * $5 = $10 for every A. However, we know his reward for every A could be (2x) doubled if he obtains at least two A + . This means 2 * $10 = $20 for every A if Paul gets at least two A + . We learn here then that Paul will get a higher reward for obtaining A grades ($20) than getting A + grades ($15) as long as he's able to score at least two A + . To maximize his payout, Paul will need to get only (2) two A + from his 10 courses. Therefore he should aim to get an A in the remaining 10 - 2 = 8 courses. Assuming Paul can get two A + and eight A in his next scorecard his total payout would be 2 * $15 + 8 * $20. This translates into $30 + $160 or $190. Final answer: 190.