The sum of 2 numbers is 32.when 5 subtracted from 4 times 1 of the numbers,the result is 8 times the other number.find the difference between the 2 numbers.
x+y = 32
4x-5 = 8y
Solve for x and y, then x-y
What are solving it is total rubbish
4x-5=8y
4x+8y=5
Jeez
To find the difference between the two numbers, let's assign variables to them. Let's call one number 'x' and the other number 'y'.
From the given information, we can form two equations:
1) The sum of the two numbers is 32:
x + y = 32
2) When 5 is subtracted from 4 times one of the numbers, the result is 8 times the other number:
4x - 5 = 8y
Now we have a system of two linear equations. To solve them, we can use the method of substitution or elimination.
Let's use the elimination method:
Multiply the first equation by 4 to make the coefficients of 'x' the same:
4x + 4y = 128
Now we have the following equations:
4x + 4y = 128
4x - 5 = 8y
Subtract the second equation from the first equation:
(4x + 4y) - (4x - 5) = 128 - 0
4y + 5 = 128
Rearrange the equation to isolate 'y':
4y = 128 - 5
4y = 123
y = 123/4
y = 30.75
Now substitute the value of 'y' into the first equation to find 'x':
x + 30.75 = 32
x = 32 - 30.75
x = 1.25
So, we have found that one number is approximately 1.25 and the other number is approximately 30.75.
To find the difference between the two numbers, subtract the smaller number from the larger number:
Difference = Larger Number - Smaller Number
Difference = 30.75 - 1.25
Difference = 29.5
Therefore, the difference between the two numbers is 29.5.
Well, well, well, it sounds like we have some number detective work to do here! Let's get cracking!
Let's call the two numbers "x" and "y." According to our first clue, the sum of these numbers is 32, so we can write the equation x + y = 32.
Now, for our second clue: "When 5 is subtracted from 4 times one of the numbers, the result is 8 times the other number." That will be x - 5 = 8y.
Now we have a system of equations! Let's solve it using our top-secret clowny math skills. Are you ready for this?
I'm going to use the first equation to solve for x: x = 32 - y.
Now let's substitute this into the second equation: (32 - y) - 5 = 8y.
Let's simplify: 27 - y = 8y.
Brace yourself, the moment of truth is here - we'll collect like terms: 27 = 9y.
And finally, we divide both sides by 9 to get: y = 3.
Now that we've found the value of y, we can substitute it back into the first equation to find x: x + 3 = 32, so x = 29.
The two numbers are 29 and 3. And the difference between them is 29 - 3 = 26.
So, voila! The difference between the two numbers is 26. Ta-da!
X+y=32
4x-5=8y
X=32-y
4(32-Y)=8y
128-4Y=8y
128=12y
Y=32/3
x+y=32
x+32/3=32
x=32-32/3
x=64/3, y=32/3