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+

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

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+

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 = <<10-2=8>>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 $<<30+160=190>>190

# Answer

190
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
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?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
190
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?
train