Here is the problem:

A two-digit number is eight times the sum of its digits.When the number is added to the number obtained by reversing the digits,the sum is 99. Find the original number.
Please explain hot to solve it and it would help a lot to if you explain other algebra word problems like:
Distance rate and time problems,Mixture Problems,wind and water current problems,work problem,area problem,cost and value problems if you could explain or give a link to something helpful,
Thanks

nm

write two digit number nm as m + 10 n

m + 10n = 8 (n+m)
and
m + 10n + n + 10 m = 99
then solve the two equations
2 n = 7 m
11n+11m = 99 or n+m=9

n = (7/2)m
(7/2)m + m = 9
7 m + 2 m =18
9 m = 18
m = 2
n = 7
number = 72

This is a question with two equations, x, y each representing one of the two digits.

the number is equal to 8 times the sum of its digits, therefore:
10x+y = 8(x+y), or
2x=7y
x=3.5y
That leaves only one solution: x=7, y=2.

When the number is added to that with the digits reversed, it should add up to 99:
72+27=99 OK.

To solve the given problem of finding the two-digit number, let's break it down step by step.

Step 1: Let's assume the original number is composed of the tens digit (T) and the units digit (U). So, the two-digit number can be represented as 10T + U.

Step 2: We are given that the number is eight times the sum of its digits. The sum of the digits can be represented as T + U. So, we can write the equation:

10T + U = 8(T + U)

Step 3: Expand the equation by distributing 8 to T and U:

10T + U = 8T + 8U

Step 4: Bring similar terms together:

10T - 8T = 8U - U

2T = 7U

Step 5: Since T and U are both digits, the possible values for T are 1, 2, 3, 4, 5, 6, 7, 8, 9. We can substitute these values one by one and see which value of T and U satisfies the equation.

Let's start by assuming T = 1:

2(1) = 7U
2 = 7U (Not possible, as U cannot be a fractional value)

Then assume T = 2:

2(2) = 7U
4 = 7U (Not possible, as U cannot be a fractional value)

Continue this process until you find a value of T and U that satisfies the equation.

For additional help with other algebra word problems, you can refer to the following resources:

1. Distance, Rate, and Time Problems:
- Khan Academy: https://www.khanacademy.org/math/algebra/quadratics/distance-and-midpoints/v/distance-rate-time-word-problems

2. Mixture Problems:
- MathIsFun: https://www.mathsisfun.com/algebra/mixture-problems.html

3. Wind and Water Current Problems:
- Purplemath: http://www.purplemath.com/modules/navalprob2.htm

4. Work Problems:
- Math.com: http://www.math.com/examples/algebra1/work.htm

5. Area Problems:
- Mathwarehouse: https://www.mathwarehouse.com/geometry/area/problem-word/index.php

6. Cost and Value Problems:
- Algebra-class: https://www.algebra-class.com/algebra-worksheets.html

By referring to these resources, you will find detailed explanations and practice problems for various types of algebra word problems.