Two numbers total 43 and have a difference of 21. Find the two numbers
x+y = 43
x-y = 21
add them
2x = 64
x = 32
then y = 43-32 = 11
x=32 , y=11
Well, let's call the two numbers x and y. We know that x + y = 43, and the difference between the two numbers is 21.
So, we can set up a system of equations:
x + y = 43
x - y = 21
To solve this, we can eliminate one of the variables by adding the two equations together:
(x + y) + (x - y) = 43 + 21
2x = 64
Now, let's solve for x:
2x = 64
x = 32
Since we know x + y = 43, we can substitute 32 for x:
32 + y = 43
y = 43 - 32
y = 11
So, the two numbers are 32 and 11. They add up to 43 and have a difference of 21.
Let's assume that one number is x, and the other number is y.
Based on the given information, we can set up two equations:
Equation 1: x + y = 43
Equation 2: x - y = 21
To solve the equations, we can use the method of substitution or elimination.
Let's solve using the substitution method.
We rearrange Equation 2 to solve for x:
x = 21 + y
Now we substitute this value of x into Equation 1:
(21 + y) + y = 43
21 + 2y = 43
2y = 43 - 21
2y = 22
Divide both sides of the equation by 2:
y = 22 / 2
y = 11
Now plug the value of y back into Equation 1:
x + 11 = 43
x = 43 - 11
x = 32
Therefore, the two numbers are 32 and 11.
To find the two numbers, let's consider the following steps:
1. Assign variables to represent the two numbers. Let's call them "x" and "y".
2. Translate the given information into mathematical equations:
- The sum of the two numbers is 43, so we have the equation: x + y = 43.
- The difference between the two numbers is 21, so we have the equation: x - y = 21.
3. We now have a system of two equations. We can solve this system for the variables "x" and "y" using either substitution or elimination method.
Let's use the elimination method:
- Multiply the second equation by -1 to get: -x + y = -21.
- Now, add the two equations together: (x + y) + (-x + y) = 43 + (-21).
This simplifies to 2y = 22.
4. Solve the equation for "y" by dividing both sides by 2: y = 22/2 = 11.
5. Substitute the value of "y" (11) into one of the original equations to solve for "x". Let's use the first equation: x + 11 = 43.
6. Solve the equation for "x" by subtracting 11 from both sides: x = 43 - 11 = 32.
7. So, the two numbers are 32 and 11.