What are the two numbers if their sum is 70 and one number is four times larger than the other?

To solve the problem, we need to set up a couple of equations based on the information provided.

Let’s denote the two numbers as:

• x = the smaller number
• y = the larger number

According to the problem:

1. The sum of the two numbers is 70:
2. x + y = 70
3. One number is four times the other:
4. y = 4x

Now we can substitute the expression for y from the second equation into the first equation:

x + 4x = 70

Simplifying, we have:

5x = 70

Now, divide both sides by 5:

x = 14

Now that we have the value of x, we can find y:

y = 4x = 4 * 14 = 56

So the two numbers are:

• x = 14 (the smaller number)
• y = 56 (the larger number)

In conclusion, the two numbers that satisfy both conditions are 14 and 56.