These are extra credit questions, and I just want to know how to solve them.
1) The sum of two-digits of a two digit number is 14. If the number represented by reversing the digits is subtracted from the original number, the result is 18. What us the orinal number?
2) If 27 is added to a two-digit number, the result is a number with the same digits, but in reverse order. The sum of the digts is 11. What is the original number?
1)Let the two digits be A and B, with A being the first digit.
A + B = 14
10A + B - (10B + A) = 18
9A -9B = 18
A - B = 2
2A = 16
A = 8
B = 6
The first two-digit number is 86.
2) Use a similar procedure for #2
A + B = 11
10A + B + 27 = 10 B + A
9A -9B +27 = 0
You finish it
if five times the successor of a number is added to an original number the sum is 83
To solve these extra credit questions, we will use a systematic approach. Let's break down each question and devise a step-by-step plan to find the solution.
1) The sum of two digits of a two-digit number is 14. If the number represented by reversing the digits is subtracted from the original number, the result is 18. What is the original number?
Step-by-step plan:
1. Let's assume the tens digit of the original number is represented by 'x' and the units digit is represented by 'y'. So the original number can be written as 10x + y.
2. We know that x + y = 14 because the sum of the two digits is 14.
3. We are also given that the reversed number subtracted from the original number gives us 18: (10x + y) - (10y + x) = 18.
4. Simplifying this equation, we get 9x - 9y = 18.
5. Dividing both sides by 9, we find x - y = 2.
6. Now, we have a system of equations: x + y = 14 and x - y = 2. We can solve this system to find the values of x and y.
7. Add the equations x + y = 14 and x - y = 2. The 'y' terms cancel out, leaving us with 2x = 16.
8. Dividing both sides by 2, we find x = 8.
9. Substitute x = 8 into one of the original equations, x + y = 14. We find 8 + y = 14, which implies that y = 6.
10. Therefore, the original number is 86.
2) If 27 is added to a two-digit number, the result is a number with the same digits, but in reverse order. The sum of the digits is 11. What is the original number?
Step-by-step plan:
1. Let's assume the tens digit of the original number is represented by 'x' and the units digit is represented by 'y'. So the original number can be written as 10x + y.
2. We are given that if 27 is added to the original number, the result has the same digits but in reverse order. It means (10x + y) + 27 gives (10y + x).
3. Simplifying this equation, we get 9x - 9y = -27.
4. Dividing both sides by 9, we find x - y = -3.
5. We are also given that the sum of the digits is 11: x + y = 11.
6. Now, we have a system of equations: x - y = -3 and x + y = 11. We can solve this system to find the values of x and y.
7. Add the equations x - y = -3 and x + y = 11. The 'y' terms cancel out, leaving us with 2x = 8.
8. Dividing both sides by 2, we find x = 4.
9. Substitute x = 4 into one of the original equations, x + y = 11. We find 4 + y = 11, which implies that y = 7.
10. Therefore, the original number is 47.