Answer: 940 people is the maximum
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Explanation:
n = 1 means 20n = 20*1 = 20 members total, which is 4 short of making a row of 26 (so the remainder is 20)
n = 2 means 20n = 20*2 = 40 members. 40/26 = 1 remainder 14. We could make one full row with 14 members left over.
20n < 1000 solves to n < 50 after dividing both sides by 20. This means n is smaller than 50. It has to be larger than 0 or else 20n would be 0 or negative. We can write 0 < n < 50 to specify the range for n.
Since n < 50, this means the largest n can get is n = 49.
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If n = 49, then 20n = 20*49 = 980
980/26 = 37 remainder 18, which isn't the remainder we want (of 4).
If n = 48, then 20n = 20*48 = 960
960/26 = 36 remainder 24, again not the remainder we want
If n = 47, then 20n = 20*47 = 940
940/26 = 36 remainder 4
If we have 940 members, then we can form 36 rows (26 in each row). So 26*36 = 936 people so far. Then we have 940-936 = 4 people left over.
There are other solutions as well such as n = 34, n = 21, and n = 8. Though n = 47 is the largest n possible to fit all the conditions required.
