If 45 is subtracted from twice the greater of two numbers, it result in the other number. If 21 is subtracted from twice the smaller number, it result in the greater number. Find the number.?

Question

Answer

Let greater no. be x
then smaller no.=(2x-45)

AtQ,
X=2(2x-45)-21

x=4x-90-21

3x=111

x=37

so,greater no.=37

Smaller no.=(2×37-45)=29. ..

Answer

Problem:
If 45 is subtracted from twice the greater of two numbers, it results in the other number. If 21 is subtracted from twice the smaller number, it results in the greater number. Find the numbers.

Given:
Let's assume the two numbers as x and y.

1. 45 subtracted from twice the greater number is equal to the other number:
2x - 45 = y

2. 21 subtracted from twice the smaller number is equal to the greater number:
2y - 21 = x

Solution:
To find the values of x and y, we'll solve the given equations simultaneously.

Step 1: Rewrite the equations:
2x - y = 45
2y - x = 21

Step 2: Solve the system of equations:
We can solve the equations using the method of substitution or elimination. Let's use the elimination method to find the solution.

Step 2.1: Multiply the first equation by 2 and the second equation by -1 to eliminate x:
4x - 2y = 90
-2y + x = -21

Step 2.2: Add the equations together:
4x - 2y + (-2y + x) = 90 + (-21)
5x - 4y = 69

Step 2.3: Solve for x:
5x = 4y + 69
x = (4y + 69) / 5

Step 3: Substitute the value of x into one of the original equations:
2y - ((4y + 69) / 5) = 21

Step 3.1: Simplify the equation:
10y - 4y - 69 = 105
6y = 174
y = 29

Step 4: Substitute the value of y into the first equation to find x:
2x - 29 = 45
2x = 74
x = 37

Answer:
The two numbers are 37 and 29.

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