Solve by setting up the proper equation to describe the facts given and then carrying out the mathematical calculations to solve for the unknown variable(s).
The difference between two numbers is 3, and the sum of those two numbers is 21. What are the two numbers?
x - y = 3
x + y = 21
x = 3 + y
3 + y + y = 21
2y = 18
y = 9
x - 9 = 3
x = 12
x-y=3
To solve this problem, we can set up two equations based on the information given.
Let's represent the two numbers as x and y.
1. The difference between two numbers is 3:
x - y = 3 (Equation 1)
2. The sum of the two numbers is 21:
x + y = 21 (Equation 2)
Now, we can solve this system of equations. There are multiple methods to solve it, but we will use the method of substitution.
From Equation 1, we can express x in terms of y:
x = y + 3
Substituting this expression for x in Equation 2, we get:
(y + 3) + y = 21
2y + 3 = 21
2y = 21 - 3
2y = 18
y = 18/2
y = 9
Now, we can substitute the value of y back into Equation 1 to find x:
x - 9 = 3
x = 3 + 9
x = 12
So, the two numbers are x = 12 and y = 9.
To solve this problem, we can set up two equations based on the given information.
Let's call the two numbers we are trying to find "x" and "y".
From the first statement, we know that the difference between the two numbers is 3. This can be expressed as:
x - y = 3 -------------- Equation 1
From the second statement, we know that the sum of the two numbers is 21. This can be expressed as:
x + y = 21 -------------- Equation 2
Now we have a system of two equations with two variables. We can solve this system using various methods. Here, I'll show you how to solve it using the method of substitution:
From Equation 1, we can rearrange it to solve for x in terms of y:
x = y + 3
Now we substitute this value of x into Equation 2:
(y + 3) + y = 21
Simplifying the equation:
2y + 3 = 21
Next, we isolate the variable y by subtracting 3 from both sides:
2y = 21 - 3
2y = 18
Dividing both sides by 2:
y = 9
Now that we have the value of y, we can substitute it back into Equation 1 to solve for x:
x - 9 = 3
Adding 9 to both sides:
x = 3 + 9
x = 12
Therefore, the two numbers are 9 and 12, respectively.