Here's the question I'm having trouble with. Please walk me completely through the question and give me the answer so I can thoroughly understand it, so I can solve similar problems in the future.

Question

#1: Mary uses a secret code to write messages. First, she translates each letter into a number based on its position in the alphabet, so that A=1, B=2, C=3, etc. Then, she multiplies this number by her favorite number and adds her mothers favorite number. Using her secret code, F becomes 65 and T becomes 177.

a. Find what number M becomes without finding Mary's favorite number.

b. What is Mary's favorite number and her mother's favorite number?

Thanks in advance. Any help is appreciated, even if you can only solve part of it. Thank you!

Answer 1

let M be moms number, and N be mary's number.

then, you need the find what is F and T in the alphabet. Check me, but I think F is 6 and T is 20.

N*6+M=65
N*20+M=177

subtract the first equation from the second..

14N=112 solve that for Marys number, and then use either equation to find Moms number.

for part a, M is in the alphabet 13.

So
N*13+M=?
but you know
N*6+M=65
N*20+M=177

subtract equation 2 from 1), and
7N=?-65 double it
14N=2?-130

Now subtract equation 2 from 3
14N=112

subtracting the last from the one before it..
0=2?-130-112 or
2?=242 and you solve for ?