Assume a is not divisible by 10. (otherwise the problem is trivial).
<span>Define R(m) to be the remainder of a^m when divided by 10. </span>
<span>R can take on one of 9 possible values, namely, 1,2,...,9. </span>
<span>Now, consider R(1),R(2),......R(10). At least 2 of them must have the sames value (by the Pigeonhole Principle), say R(i) = R(j) ( j>i ) </span>
<span>Then, a^j - a^i is divisible by 10.</span>
Ok so if 1200 total pens and 60 were taken that's a ratio of 1200/60=20
out of 60pens 4 didn't work, again ratio is 4/60=1/15 so about 1/15 of the pens didn't work.
so we have 1200pens * 1/15broken ratio = 80 pens or we can say
20*4=80pens won't work from 20 groups of 60 and 4 out of 60 not working is 20*4=80 not working from total batch of 1200.
hope this helps you some! thank you!!!!!!!!!
Answer:
1600 after 24 hours
Step-by-step explanation:
100+100 = 200 after 6 hours
200+200 = 400 after 12 hours
400+400 = 800 after 18 hours
800+800 = 1600 after 24 hours
35a + 25c = 2660
a = 2c
35(2c) + 25c = 2660
70c + 25c = 2660
95c = 2660
c = 2660/95
c = 28 <=== there were 28 children tickets
a = 2c
a = 2(28)
a = 56 <== there were 56 adult tickets
