What are the two numbers if their sum is 40 and their difference is 10?

To find the two numbers, let’s denote the two unknowns as x and y.

We have the following two equations based on the problem:

• x + y = 40 (Equation 1: The sum of the two numbers is 40)
• x – y = 10 (Equation 2: The difference of the two numbers is 10)

We can solve these equations using the elimination or substitution method. Here’s how you can solve it step-by-step:

Step 1: Solve for one variable

Let’s solve for x in terms of y using Equation 1:

x = 40 - y

Step 2: Substitute into the second equation

Next, substitute x in Equation 2 with the expression we just found:

(40 - y) - y = 10

Now simplify this equation:

40 - 2y = 10

Step 3: Solve for y

Now, let’s isolate y:

-2y = 10 - 40
-2y = -30
y = 15

Step 4: Find x

Now that we have y, we can find x by substituting y back into the equation we found earlier:

x = 40 - 15
x = 25

Conclusion

Thus, the two numbers are x = 25 and y = 15. To verify:

• Sum: 25 + 15 = 40 ✔️
• Difference: 25 – 15 = 10 ✔️

Everything checks out, so the final answer is:

The two numbers are 25 and 15.