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?
How much would Paul get for a B+? ** 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 = $<<2*5=10>>10 for a B+ if Paul gets at least two A+
How much would Paul get for an A? ** We know Paul would get twice the reward of a B+ if he gets an A. This means 2*$5 = $<<5*2=10>>10 for every A
How much would Paul get for an A? ** However, we know his reward for every A could be (2x) doubled if he obtains at least two A+. This means 2*$10 = $<<2*10=20>>20 for every A if Paul gets at least two A+
How much would Paul get for an 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+.
How many A+ does Paul need? ** 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 = <<10-2=8>>8 courses
How much would Paul get for his next scorecard? ** Assuming Paul can get two A+ and eight A in his next scorecard his total payout would be 2*$15 + 8*$20
How much would Paul get for his next scorecard? ** This translates into $30 + $160 or $<<30+160=190>>190
#### 190