The sum of two numbers is 57 and the difference is 23 . What are the numbers?
80
Let's call the first number x and the second number y. We are given two pieces of information:
1. The sum of the two numbers is 57, so we can write this as an equation: x + y = 57.
2. The difference between the two numbers is 23, so we can write this as another equation: x - y = 23.
We now have a system of two equations with two variables. To solve for x and y, we can use the method of substitution or elimination.
Let's solve using the substitution method:
From the first equation, x + y = 57, we can isolate one variable. Let's solve for y:
y = 57 - x.
Now substitute this value of y into the second equation:
x - (57 - x) = 23.
Simplify the equation:
x - 57 + x = 23.
Combine like terms:
2x - 57 = 23.
Add 57 to both sides of the equation to isolate the x term:
2x = 23 + 57.
Simplify:
2x = 80.
Divide both sides by 2:
x = 40.
Now substitute this value of x back into the first equation to solve for y:
40 + y = 57.
Subtract 40 from both sides:
y = 17.
So the two numbers are 40 and 17.
To find the two numbers, we can set up a system of equations based on the given information.
Let's assume the two numbers are x and y.
From the given information, we know that the sum of the two numbers is 57, so we can write the equation:
x + y = 57 ----(equation 1)
We also know that the difference between the two numbers is 23, so we can write the equation:
x - y = 23 ----(equation 2)
Now we have a system of two equations with two variables (x and y). We can solve this system to find the values of x and y.
One approach to solve this system is by using the method of substitution. We can solve equation 1 for x in terms of y, and then substitute that expression into equation 2.
From equation 1, we have:
x = 57 - y
Substituting this value of x into equation 2, we get:
57 - y - y = 23
Simplifying this equation, we have:
57 - 2y = 23
Now, we can solve for y by isolating it on one side of the equation. Subtracting 57 from both sides, we get:
-2y = 23 - 57
Simplifying further, we have:
-2y = -34
Dividing both sides by -2, we get:
y = (-34) / (-2)
y = 17
Now that we know the value of y, we can substitute it back into equation 1 to find x:
x + 17 = 57
Subtracting 17 from both sides, we get:
x = 57 - 17
x = 40
Therefore, the two numbers are 40 and 17.
Solve the following two equations by first adding them
Things fall apart just nicely
x+y = 57
x-y = 23