4. The sum of two numbers is 50. If twice the larger is subtracted from 4 times the smaller the result is 8. Find the numbers
is it this x+x(2x-4=8)=50
Let x = larger number.
y = smaller number
x + y = 50
4y - 2x = 8
2x + 8 = 4y = 4 (50 - x)
2x + 8 = 200 - 4x
6x = 192
x = 32
y = 18
Well, well, well, it seems like we have a math problem on our hands! Let's tackle it with some humor, shall we?
First, let's establish our two numbers. We'll call the smaller number "x" and the larger number "y". Remember, the sum of these two numbers is 50.
Now, let's translate the second part of the problem into math speak. "Twice the larger is subtracted from 4 times the smaller, and the result is 8." In equation form, that would be:
4x - 2y = 8.
We also know that x + y = 50.
Now, it's time to solve this riddle! Let's use some math humor along the way!
Step 1: We have two equations:
4x - 2y = 8,
x + y = 50.
Step 2: Let's solve the second equation for x:
x = 50 - y.
Step 3: Substitute the value of x from step 2 into the first equation:
4(50 - y) - 2y = 8.
(200 - 4y) - 2y = 8.
200 - 4y - 2y = 8.
200 - 6y = 8.
Step 4: Let's solve for y:
-6y = 8 - 200.
-6y = -192.
y = -192 / -6.
y = 32.
Step 5: We can find x by substituting the value of y into the second equation:
x + 32 = 50.
x = 50 - 32.
x = 18.
So, the two numbers are 18 and 32. Voila! We made it through the math maze! Keep up the laughs and never be afraid to clown around with numbers!
To solve this problem, let's assign variables to the two numbers. Let's call the smaller number 'x' and the larger number 'y'.
We are given two pieces of information:
1. The sum of the two numbers is 50: x + y = 50.
2. Twice the larger is subtracted from 4 times the smaller and the result is 8: 4x - 2y = 8.
Using these equations, we can create a system of linear equations and solve for the values of 'x' and 'y'.
Let's start with the first equation:
x + y = 50
Now, let's rearrange the second equation to solve for one variable in terms of the other:
4x - 2y = 8
2x - y = 4
We have two equations:
1. x + y = 50
2. 2x - y = 4
Now we can solve the system of equations using either substitution or elimination. Let's use the substitution method:
From the first equation, we can solve for 'y' in terms of 'x':
y = 50 - x
Substitute this expression for 'y' into the second equation:
2x - (50 - x) = 4
Simplify and solve for 'x':
2x - 50 + x = 4
3x - 50 = 4
3x = 4 + 50
3x = 54
x = 54/3
x = 18
Now substitute the value of 'x' back into the first equation to solve for 'y':
18 + y = 50
y = 50 - 18
y = 32
So, the smaller number is 18 and the larger number is 32.
To solve this problem, let's simplify the given information step by step.
Let's assume that the smaller number is denoted by "x" and the larger number is denoted by "y", where y > x.
According to the problem, the sum of the two numbers is 50, so we can write the equation:
x + y = 50 (Equation 1)
The problem also states that if twice the larger number is subtracted from 4 times the smaller number, the result is 8. This can be expressed as:
4x - 2y = 8 (Equation 2)
Now we have a system of equations:
x + y = 50 (Equation 1)
4x - 2y = 8 (Equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Using the method of elimination, we can multiply Equation 1 by 2 to match the coefficients of "y" in both equations:
2(x + y) = 2(50)
2x + 2y = 100
Now we have:
2x + 2y = 100 (Equation 3)
4x - 2y = 8 (Equation 2)
Adding Equation 3 and Equation 2, we eliminate the variable "y":
2x + 2y + 4x - 2y = 100 + 8
6x = 108
Dividing both sides of the equation by 6, we get:
x = 108/6
x = 18
Now that we have the value of "x", we can substitute it back into Equation 1 to find the value of "y":
18 + y = 50
Subtracting 18 from both sides:
y = 50 - 18
y = 32
Therefore, the two numbers are 18 and 32.