To solve this problem, we need to set up a couple of equations based on the information given.
Let’s call the smaller number x. According to the problem, the larger number is 4 times as large as the smaller number, so we can express the larger number as 4x.
Next, we know that the sum of these two numbers equals 40. We can set up the equation:
x + 4x = 40
This simplifies to:
5x = 40
Now, we can solve for x by dividing both sides of the equation by 5:
x = 40 / 5
x = 8
So, the smaller number is 8. To find the larger number, we can substitute x back into the expression for the larger number:
4x = 4 * 8 = 32
Now we have both numbers:
- Smaller number: 8
- Larger number: 32
In conclusion, the two numbers that satisfy the conditions of the problem are 8 and 32.