In a two-digit number the units’ digit is 7 more than the tens’ digit. The number with digits reversed is three times as large as the sum of the original number and the two digits. Find the number.
Why do you need such fast help?
I need fast help because i have to go somewhere and i need someone to help me with my math
The number is either 18 or 29.
Which of these numbers fulfills the other criteria?
its 18 thx
Yes, 18. You're welcome.
To solve this problem, let's break it down step by step.
1. Let's represent the tens digit by the variable 'x' and the units digit by 'y'. We are given that the units digit is 7 more than the tens digit, so we can express this as y = x + 7.
2. The original number can be written as 10x + y, since the tens digit is in the tens place and the units digit is in the ones place.
3. The number with digits reversed is given as yx, which is 10y + x.
4. According to the problem, the number with digits reversed is three times as large as the sum of the original number and the two digits. Mathematically, we can express this as the equation 10y + x = 3(10x + y + x + y).
5. Simplifying the equation, we have 10y + x = 3(12x + 2y).
6. Expanding the right side of the equation, we get 10y + x = 36x + 6y.
7. Rearranging the equation, we have 9y - 35x = 0.
Now, we have a system of equations:
y = x + 7
9y - 35x = 0
To solve this system, we can substitute the value of y from the first equation into the second equation.
8. Substitute y = x + 7 into 9y - 35x = 0:
9(x + 7) - 35x = 0.
9. Expanding and simplifying the equation, we get:
9x + 63 - 35x = 0.
10. Combine like terms:
-26x + 63 = 0.
11. Move 63 to the other side of the equation:
-26x = -63.
12. Divide both sides by -26:
x = -63 / -26.
13. Simplifying the fraction, we have:
x = 63 / 26.
14. We can express x as a simplified fraction: x = 21 / 13.
15. Now, substitute this value of x back into the first equation to find y:
y = (21 / 13) + 7.
16. Simplifying the equation, we have:
y = 21 / 13 + 91 / 13.
17. Combining the fractions, we get:
y = 112 / 13.
Therefore, the tens digit (x) is 21/13 and the units digit (y) is 112/13. The number can be expressed as 10x + y, so substituting the values we found, the number is 10(21/13) + (112/13).
To get the final answer, multiply 10 by 21/13 and add 112/13 to it. The result will be the number you're looking for.