Question

M And N are two-digit natural numbers greater than 15. M leaves a remainder of 2 when divided by 4 while N is odd. They satisfy the equation below. MN=9M+14N+450. How many ordered pairs (m,n) exist?​

Answer 1

Answer:- The number 3
m
+7
n
is divisible by 10 only when the last digit of both add up to make 10
In this case it is possible only when 3
m
ends with 9 and 7
n
ends with 1 or vice-versa.Also when 3
m
ends with 3 and 7
n
ends with 7 and vice-versa.
3
m
ends with 9 when m=2,6,10,14,18 and 7
n
ends with 1 when n=4,8,12,16,20
Hence no. of ways the addition results 10=5×5=25
Similarly 3
m
ends with 1 when m=4,8,12,16,20 and7
n
ends with 9 when n=2,6,10,14,18
Hence no. of ways the addition results 10=5×5=25
Similarly in other two cases also we can see that the addition results 10 in 5×5=25 ways.
Therefore, total number of (m,n) pairs=4×25=100
Hopeit helps!!
Plz mark me as the brainliest answer....