Find the value of M

M is a positive number that follow these conditions:

• M is a number that 80<M<100 
• if M divided by 4 the remainder is 3 
• and if M divided by 5 the remainder is 1.

Find the value of M?

Solution:

• M divided by 4 gives remainder 3. So M can be written as 4r + 3 for some integer r
• M divided by 5 gives remainder 1. So M can be written as 5*t + 1 for some integer t

So M=4*r + 3 or M=5*t + 1

• But  80<M<100 

Thus 80<4*r + 3<100 , 77<4r<97 , 19.25<r<24.25 so r={20,21,22,23,24}

• r=20 => M=4*20+3=83 
• r=21 => M=4*21+3=87
• r=22 => M=4*22+3=91
• r=23 => M=4*23+3=95
• r=24 => M=4*24+3=99

Only r=22 that M=91 can be written as 91=5*18+1  so the only one value of M=91 that apply to these two forms.