Estimate a 20% tip on a dinner bill of $171.81 by first rounding the bill amount to the nearest ten dollars.
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If is a number that is both divisible by 4 and 5, then
4 and 5 are coprime, so we can use the Chinese remainder theorem to solve this system and find that is a solution to the system, where
is any integer. Simply put, any multiple of 20 fits the bill.
Now, there are 11 numbers between 100 and 300 that are divisible by 20 (100, 120, 140, and so on). We have when
, so the sum we want to compute is