two numbers have the sum of 39 the difference is 11 what are the two numbers?
Let x = the larger number.
x + (x - 11) = 39
2x - 11 = 39
2x = 50
x = ?
25
Let's solve this step by step.
Step 1: Let's assume the two numbers as x and y.
Step 2: According to the given information, the sum of the two numbers is 39, which can be expressed as:
x + y = 39 ... (equation 1)
Step 3: The difference between the two numbers is 11, which can be expressed as:
x - y = 11 ... (equation 2)
Step 4: Now we have a system of equations. To solve this, we can use the method of substitution.
Step 5: Solve equation 2 for x:
x = y + 11
Step 6: Substitute the value of x from equation 5 into equation 1:
y + 11 + y = 39
Step 7: Combine like terms:
2y + 11 = 39
Step 8: Subtract 11 from both sides:
2y = 28
Step 9: Divide both sides by 2:
y = 14
Step 10: Substitute the value of y into equation 2 to find x:
x - 14 = 11
x = 11 + 14
x = 25
Step 11: Therefore, the two numbers are 25 and 14.
To find the two numbers, let's use a system of equations:
Let's call the first number x and the second number y.
From the given information,
x + y = 39 (equation 1)
x - y = 11 (equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Method 1: Substitution
We'll solve equation 2 for x:
x = 11 + y
Now, substitute this expression into equation 1:
11 + y + y = 39
Combine like terms:
2y + 11 = 39
Move 11 to the other side of the equation:
2y = 39 - 11
2y = 28
Divide both sides by 2:
y = 28 / 2
y = 14
Now, substitute the value of y back into equation 1:
x + 14 = 39
Move 14 to the other side of the equation:
x = 39 - 14
x = 25
So, the two numbers are 25 and 14.
Method 2: Elimination
Add both equations together:
(x + y) + (x - y) = 39 + 11
Simplify:
2x = 50
Divide both sides by 2:
x = 50 / 2
x = 25
Now, substitute the value of x back into equation 1:
25 + y = 39
Move 25 to the other side of the equation:
y = 39 - 25
y = 14
So, the two numbers are 25 and 14.
Using either method, we found that the two numbers are 25 and 14.