Final answer:
To solve the problem, we set up two equations based on the given information and find that the smaller number is 37 and the larger number is 185.
Step-by-step explanation:
The problem states that one positive number is 5 times another number and the difference between the two numbers is 148. We can set up two equations to solve this problem. Let's call the first number x and the second number y. According to the problem, we have:
- x = 5y (Equation 1)
- x - y = 148 (Equation 2)
We can substitute Equation 1 into Equation 2, so it becomes:
5y - y = 148
4y = 148
Now we can find y by dividing both sides by 4:
y = 148 / 4
y = 37
Using Equation 1, we can then calculate x:
x = 5 × 37
x = 185
Therefore, the two numbers are 37 and 185.