Finding Two Numbers
To solve the problem where the sum of two numbers is 21 and their difference is 5, we can use a system of equations. Let’s denote the two numbers as x and y.
We can set up the following equations based on the information given:
- Equation 1: x + y = 21
- Equation 2: x – y = 5
Now, we can solve these equations step-by-step:
Step 1: Solve Equation 2 for x
From Equation 2, we can express x in terms of y:
x = y + 5
Step 2: Substitute into Equation 1
Next, we substitute this expression for x back into Equation 1:
(y + 5) + y = 21
Combine like terms:
2y + 5 = 21
Step 3: Solve for y
Now, isolate y:
2y = 21 – 5
2y = 16
y = 16 / 2
y = 8
Step 4: Solve for x
Having found y, we can now find x using our expression from Step 1:
x = 8 + 5
x = 13
Conclusion
The two numbers are:
- x = 13
- y = 8
Thus, the numbers that satisfy the condition that their sum is 21 and their difference is 5 are 13 and 8.