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A) Given that x is a positive integer less than 100, how many solutions does the congruence x+13=55 (mod 34) have?

 

 

B)Donna has n boxes of doughnuts. Each box contains 13 doughnuts.

After eating one doughnut, Donna is able to rearrange the remaining doughnuts into bags so that each bag contains 9 doughnuts, and none are left over. What is the smallest possible value of n?

 

TXXS!!!!!!!!!

 Dec 9, 2018
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something equalling 55 (mod 34) is unusual to say the least as 55 mod 34 = 21

 

do you mean x+13=21 (mod 34) ?

 

clearly x = 8 + 34k which gives 8, 42, 76 begin less than 100

 

so 3 solutions

 

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13n-1 = 9k

 

13n-9k = 1

 

Using the Euclidean algorithm

 

13(7) - 9(10) = 91-90 = 1

 

so 7 boxes and 9 bags

 Dec 9, 2018

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