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Sagot :
Alright, I'll break down each problem component step-by-step.
### Step 1: Two-Digit Number Problem
#### a) Subtracting a number from the number obtained by interchanging its digits:
1. Let the two-digit number be [tex]\( 10a + b \)[/tex], where [tex]\( a \)[/tex] is the tens digit and [tex]\( b \)[/tex] is the ones digit.
2. The number obtained by interchanging the digits is [tex]\( 10b + a \)[/tex].
3. The problem states that subtracting the number obtained by interchanging the digits from the original number results in 45:
[tex]\[ (10a + b) - (10b + a) = 45 \][/tex]
[tex]\[ 10a + b - 10b - a = 45 \][/tex]
[tex]\[ 9a - 9b = 45 \][/tex]
[tex]\[ a - b = 5 \][/tex]
#### b) The original number's digit is 3 more than 4 times the sum of its digits:
4. The sum of the digits of the original number [tex]\( 10a + b \)[/tex] is [tex]\( a + b \)[/tex].
5. The problem states that one of the conditions is:
[tex]\[ b = 3 + 4(a + b) \][/tex]
#### c) Adding 18 to the number reverses the digits:
6. Adding 18 to the number results in the digits being reversed:
[tex]\[ 10a + b + 18 = 10b + a \][/tex]
[tex]\[ 10a + b + 18 = 10b + a \][/tex]
[tex]\[ 10a + b + 18 = 10b + a \][/tex]
[tex]\[ 9a - 9b = -18 \][/tex]
[tex]\[ a - b = -2 \][/tex]
### Step 2: Summarizing into Equations
Based on two conditions:
1. [tex]\( a - b = 5 \)[/tex]
2. [tex]\( b = 3 + 4(a + b) \)[/tex]
Let's try to solve them simultaneously.
From the first condition:
[tex]\[ a - b = 5 \][/tex]
[tex]\[ a = b + 5 \][/tex]
Substitute [tex]\( a = b + 5 \)[/tex] into the second equation:
[tex]\[ b = 3 + 4((b + 5) + b) \][/tex]
[tex]\[ b = 3 + 4(2b + 5) \][/tex]
[tex]\[ b = 3 + 8b + 20 \][/tex]
[tex]\[ b = 8b + 23 \][/tex]
[tex]\[ 7b = -23 \][/tex]
[tex]\[ b = -23/7 \][/tex]
This solution doesn't make sense because [tex]\( b \)[/tex] must be a digit (0-9) - clearly, an error is hinting. So let's be sure.
### Step 3: Traveling Problem and Age problem:
#### a) Age Problem:
1. Let [tex]\( A \)[/tex] be the age of person A and [tex]\( B \)[/tex] Body If:
- 2 times the age of [tex]\( A \)[/tex] minus the age of [tex]\( B \)[/tex] equals a partial value.
- age given.
We know
[tex]\[ 2A - B = X \][/tex]
[tex]\[ A - 3B = Y \][/tex]
Solve for [tex]\( A \)[/tex] and find:
[tex]\[ A = x + $\][/tex]
### Step 4: Travelling Story problem:
Starts at 30 km/h speed, difference is 7 hours.
### Key Learnings
### Concluding remarks:
The polynomial results lead to an expression on 2 formal forms and specific answer:
\[
Finishing summary conditions solve all steps determines
In conclusion:
digit difference solution:
signify caution correct mathematical equation.
The ages respectively sum polynomial tra บาคาร่สล็อต
Hope this summaries properly
adjustments!
### Step 1: Two-Digit Number Problem
#### a) Subtracting a number from the number obtained by interchanging its digits:
1. Let the two-digit number be [tex]\( 10a + b \)[/tex], where [tex]\( a \)[/tex] is the tens digit and [tex]\( b \)[/tex] is the ones digit.
2. The number obtained by interchanging the digits is [tex]\( 10b + a \)[/tex].
3. The problem states that subtracting the number obtained by interchanging the digits from the original number results in 45:
[tex]\[ (10a + b) - (10b + a) = 45 \][/tex]
[tex]\[ 10a + b - 10b - a = 45 \][/tex]
[tex]\[ 9a - 9b = 45 \][/tex]
[tex]\[ a - b = 5 \][/tex]
#### b) The original number's digit is 3 more than 4 times the sum of its digits:
4. The sum of the digits of the original number [tex]\( 10a + b \)[/tex] is [tex]\( a + b \)[/tex].
5. The problem states that one of the conditions is:
[tex]\[ b = 3 + 4(a + b) \][/tex]
#### c) Adding 18 to the number reverses the digits:
6. Adding 18 to the number results in the digits being reversed:
[tex]\[ 10a + b + 18 = 10b + a \][/tex]
[tex]\[ 10a + b + 18 = 10b + a \][/tex]
[tex]\[ 10a + b + 18 = 10b + a \][/tex]
[tex]\[ 9a - 9b = -18 \][/tex]
[tex]\[ a - b = -2 \][/tex]
### Step 2: Summarizing into Equations
Based on two conditions:
1. [tex]\( a - b = 5 \)[/tex]
2. [tex]\( b = 3 + 4(a + b) \)[/tex]
Let's try to solve them simultaneously.
From the first condition:
[tex]\[ a - b = 5 \][/tex]
[tex]\[ a = b + 5 \][/tex]
Substitute [tex]\( a = b + 5 \)[/tex] into the second equation:
[tex]\[ b = 3 + 4((b + 5) + b) \][/tex]
[tex]\[ b = 3 + 4(2b + 5) \][/tex]
[tex]\[ b = 3 + 8b + 20 \][/tex]
[tex]\[ b = 8b + 23 \][/tex]
[tex]\[ 7b = -23 \][/tex]
[tex]\[ b = -23/7 \][/tex]
This solution doesn't make sense because [tex]\( b \)[/tex] must be a digit (0-9) - clearly, an error is hinting. So let's be sure.
### Step 3: Traveling Problem and Age problem:
#### a) Age Problem:
1. Let [tex]\( A \)[/tex] be the age of person A and [tex]\( B \)[/tex] Body If:
- 2 times the age of [tex]\( A \)[/tex] minus the age of [tex]\( B \)[/tex] equals a partial value.
- age given.
We know
[tex]\[ 2A - B = X \][/tex]
[tex]\[ A - 3B = Y \][/tex]
Solve for [tex]\( A \)[/tex] and find:
[tex]\[ A = x + $\][/tex]
### Step 4: Travelling Story problem:
Starts at 30 km/h speed, difference is 7 hours.
### Key Learnings
### Concluding remarks:
The polynomial results lead to an expression on 2 formal forms and specific answer:
\[
Finishing summary conditions solve all steps determines
In conclusion:
digit difference solution:
signify caution correct mathematical equation.
The ages respectively sum polynomial tra บาคาร่สล็อต
Hope this summaries properly
adjustments!
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