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.
#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!
Sure, I'd be happy to help you with that problem! Let's go step by step.
Step 1: Translation
Mary translates each letter into a number based on its position in the alphabet. For example, A is 1, B is 2, C is 3, and so on. This means that the alphabet can be represented as follows: A=1, B=2, C=3, D=4, E=5, F=6, and so on.
Step 2: Multiplication and Addition
Mary multiplies the number of each letter by her favorite number and then adds her mother's favorite number. Using the information given, we can create two equations:
For F, the translation is 6. So, we can write the equation as:
6 x Mary's Favorite Number + Mary's Mother's Favorite Number = 65
For T, the translation is 20. So, we can write the equation as:
20 x Mary's Favorite Number + Mary's Mother's Favorite Number = 177
Now, let's solve these equations to find the answers.
a. To find what number M becomes without finding Mary's favorite number, we need to find the value of M when translated into a number. M is the 13th letter of the alphabet. So, M corresponds to the number 13.
To find the number M becomes using Mary's secret code, we can use the equation:
13 x Mary's Favorite Number + Mary's Mother's Favorite Number = ?
b. To find Mary's favorite number and her mother's favorite number, we can solve the two equations simultaneously.
Equation 1: 6 x Mary's Favorite Number + Mary's Mother's Favorite Number = 65
Equation 2: 20 x Mary's Favorite Number + Mary's Mother's Favorite Number = 177
Let's solve these equations together!
Using the method of substitution, we can rearrange Equation 1 to solve for Mary's Mother's Favorite Number:
Mary's Mother's Favorite Number = 65 - 6 x Mary's Favorite Number
Substituting this value into Equation 2, we get:
20 x Mary's Favorite Number + (65 - 6 x Mary's Favorite Number) = 177
Simplifying:
20 x Mary's Favorite Number + 65 - 6 x Mary's Favorite Number = 177
14 x Mary's Favorite Number + 65 = 177
14 x Mary's Favorite Number = 177 - 65
14 x Mary's Favorite Number = 112
Dividing both sides by 14, we can solve for Mary's Favorite Number:
Mary's Favorite Number = 112 / 14
Mary's Favorite Number = 8
Now that we know Mary's Favorite Number is 8, we can substitute this value back into Equation 1 to find Mary's Mother's Favorite Number:
Mary's Mother's Favorite Number = 65 - 6 x Mary's Favorite Number
Mary's Mother's Favorite Number = 65 - 6 x 8
Mary's Mother's Favorite Number = 65 - 48
Mary's Mother's Favorite Number = 17
So, the answer to Part a is that M becomes 13 x Mary's Favorite Number + Mary's Mother's Favorite Number, and the answer to Part b is that Mary's Favorite Number is 8 and Mary's Mother's Favorite Number is 17.
I hope that helps! Let me know if you have any other questions.
Sure, let's go step-by-step to solve this problem.
Step 1: Understanding the problem
We are given that Mary uses a secret code to write messages. Her code involves translating each letter into a number based on its position in the alphabet. Then she multiplies this number by her favorite number and adds her mother's favorite number. We need to find out what number M becomes without explicitly knowing Mary's favorite number. Additionally, we need to determine Mary's favorite number and her mother's favorite number.
Step 2: Analyzing the problem
To solve this problem, we will need some information about the specific letters mentioned in the question. We know that F becomes 65 and T becomes 177 in Mary's secret code. We can use this information to determine the pattern and calculate the values for M, Mary's favorite number, and her mother's favorite number.
Step 3: Solving the problem
a. Finding the number for M:
To find out the number M becomes without finding Mary's favorite number, we need to look for a pattern. Let's consider the letters for which we already know the numerical values:
F = 65
T = 177
From these examples, we can observe the following pattern:
The numerical value of a letter in Mary's code can be obtained by multiplying the position of the letter in the alphabet by Mary's favorite number and then adding her mother's favorite number.
Using this pattern, we can find the numerical value of M. M is the 13th letter in the alphabet (A=1, B=2, C=3, ..., M=13). Substituting this into the equation:
M = (position of M) * (Mary's favorite number) + (Mary's mother's favorite number)
M = 13 * (Mary's favorite number) + (Mary's mother's favorite number)
However, since we don't know Mary's favorite number and her mother's favorite number, we are unable to find the exact numerical value of M without further information.
b. Finding Mary's favorite number and her mother's favorite number:
To determine Mary's favorite number and her mother's favorite number, we need additional information from the question.
Unfortunately, the given question does not provide any additional information or equations to find Mary's favorite number and her mother's favorite number. Therefore, without further information, we cannot determine the values of Mary's favorite number and her mother's favorite number.
Overall, we are unable to find the numerical value of M without knowing Mary's favorite number, and we cannot determine Mary's favorite number and her mother's favorite number without additional information.
I hope this step-by-step explanation helps you understand the problem better, even though we were unable to solve it completely due to a lack of information. If you have any further questions, feel free to ask!
To solve this problem, we need to set up a system of equations using the given information. Let's start with part a.
a. Find what number M becomes without finding Mary's favorite number.
From the given information, we know that F becomes 65 and T becomes 177.
Let's start by translating F and T into their corresponding numbers based on their positions in the alphabet. F is the 6th letter of the alphabet, and T is the 20th letter. So we have:
First equation: F = 6
Second equation: T = 20
According to the secret code, each letter is multiplied by Mary's favorite number and then added Mary's mother's favorite number. Let's represent Mary's favorite number with 'x' and her mother's favorite number with 'y'. Using this information, we can set up the following equations:
Third equation: 6x + y = 65
Fourth equation: 20x + y = 177
To find the value of M, we need to replace it with the corresponding number based on its position in the alphabet. M is the 13th letter of the alphabet.
So let's substitute M with 13 in the equations:
Fifth equation: 13x + y
Now we can solve the system of equations to find the values of x and y and substitute them into the fifth equation to find the value of M.
To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
From the third equation, we can solve for y:
y = 65 - 6x
Now substitute this value for y in the fourth equation:
20x + (65 - 6x) = 177
Simplify the equation:
20x - 6x + 65 = 177
14x + 65 = 177
Move 65 to the other side of the equation:
14x = 177 - 65
14x = 112
Divide both sides by 14:
x = 112 / 14
x = 8
Now we have the value of x, which represents Mary's favorite number. To find y, substitute x = 8 into any of the earlier equations. Let's use the third equation:
6x + y = 65
6(8) + y = 65
48 + y = 65
Subtract 48 from both sides:
y = 65 - 48
y = 17
Now we have the values of x and y, which represent Mary's favorite number and her mother's favorite number, respectively.
Finally, substitute these values into the fifth equation to find the value of M:
13x + y = 13(8) + 17 = 104 + 17 = 121
Therefore, M becomes 121.
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 ?