Sufficient 9391

In Kocourkov, they use coins with only two values expressed in Kocourkov crowns by positive integers. With a sufficient number of such coins, it is possible to pay any integer amount greater than 53 cats’
crowns accurately and without return. However, we cannot pay 53 cat crowns without a refund.

Find out what values ​​could have been on the cat’s coins. Identify at least two solutions.

Correct answer:

a1 =  3
b1 =  28
a2 =  4
b2 =  19
a3 =  7
b3 =  10
a4 =  2
b4 =  55

Step-by-step explanation:

53 = ax + by 53 < ax + by  a1=3
b1=28 t1=18 a1+0 b1=18 3+0 28=54 t2=9 a1+1 b1=9 3+1 28=55 t3=0 a1+2 b1=0 3+2 28=56  b1=28
a2=4
b2=19 t4=4 a2+2 b2=4 4+2 19=54 t5=9 a2+1 b2=9 4+1 19=55 t6=14 a2+0 b2=14 4+0 19=56 t7=0 a2+3 b2=0 4+3 19=57 
a3=7
b3=10
a4=2
b4=55 t8=27 a4+0 b4=27 2+0 55=54 t9=0 a4+1 b4=0 2+1 55=55 t10=28 a4+0 b4=28 2+0 55=56 



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