If the sum of two numbers is 30 and their difference is 20, what are the two numbers?

To find the two numbers based on the conditions provided, we can set up a system of equations:

• Let x be the first number.
• Let y be the second number.

The two conditions specified can be expressed as:

1. x + y = 30 (the sum of the two numbers is 30)
2. x – y = 20 (the difference between the two numbers is 20)

Now, let’s solve these equations step-by-step:

Step 1: Solve for x in terms of y

From the first equation, we can express x as:

x = 30 – y

Step 2: Substitute x into the second equation

Now, we can substitute x into the second equation:

(30 – y) – y = 20

Step 3: Simplify the equation

Simplifying that gives:

30 – 2y = 20

-2y = 20 – 30

-2y = -10

y = 5

Step 4: Find x

Now, we can substitute y back into the equation we derived in Step 1:

x = 30 – 5

x = 25

Conclusion

The two numbers are:

• First number (x): 25
• Second number (y): 5

Thus, the two numbers that satisfy the conditions given are 25 and 5.