A Two number is 4 times the sum of its digits. The sum of the number formed by reversing its digits and 9 is equal to 2 times the original number. Find the number.
I assume you meant: A two digit number ...
Let the tens digit be x, let the unit digit be y
Then the originial number is 10x + y
and the number reversed is 10y + x
10x + y = 4(x+y)
10x + y = 4x + 4y
6x - 3y = 0
2x - y = 0 OR y = 2x
"The sum of the number formed by reversing its digits and 9 is equal to 2 times the original number"
---> 10y+x + 9 = 2(10x + y)
10y + x + 9 = 20x + 2y
8y = 19x - 9
8(2x) = 19x - 9
use substitution:
16x - 19x = -9
x = 3 , then y = 6
Then the original number was 36
check: is the sum of its digit equal to 9 ? YES
The number reversed is 63
is 63 + 9 = 2(36) ? , YES
All is good
To solve this problem, let's break it down into steps:
Step 1: Understand the problem:
We are given a two-digit number, and we need to find the number itself.
Step 2: Assume the number:
Let's assume the two-digit number as "10x + y", where x and y represent the tens and ones digits, respectively.
Step 3: Write the given conditions as equations:
We have two given conditions in the problem that we can translate into equations:
Condition 1: "A Two number is 4 times the sum of its digits."
This can be written as: 10x + y = 4(x + y)
Condition 2: "The sum of the number formed by reversing its digits and 9 is equal to 2 times the original number."
This can be written as: 10y + x + 9 = 2(10x + y)
Step 4: Solve the equations simultaneously:
Now we need to solve the system of equations simultaneously to find the values of x and y.
Let's solve Condition 1:
10x + y = 4x + 4y
Simplifying, we get: 6x = 3y
Dividing both sides by 3, we get: 2x = y ----(Equation 1)
Let's solve Condition 2:
10y + x + 9 = 20x + 2y
Simplifying, we get: 9y = 19x - x - 9
which can be written as: 9y = 18x - 9
Dividing both sides by 9, we get: y = 2x - 1 ----(Equation 2)
Step 5: Substitute the value of y from Equation 1 into Equation 2:
Substituting the value of y from Equation 1 into Equation 2, we get:
2x - 1 = 2x
Simplifying further, we get: -1 = 0
This means there is no solution to this system of equations. Therefore, there is no two-digit number that satisfies the given conditions.