Final answer:
The two numbers that meet the criteria of having a sum of 60 and a difference of 24 are 42 and 18. This was determined by setting up two equations based on the sum and difference and solving for the two unknowns.
Step-by-step explanation:
To solve the problem, we need to find two numbers that when added together give us 60 and when subtracted give us 24. Let's call these numbers x and y, with x being the larger number. We can set up two equations based on the information given:
- x + y = 60 (sum of the two numbers)
- x - y = 24 (difference of the two numbers)
To solve the simultaneous equations, we can add the two equations together:
2x = 84 (by adding x + y to x - y)
Now, we can find the value of x by dividing both sides of the equation by 2:
x = 42
Now that we have the value of x, we can find the value of y by substituting x into one of the initial equations:
42 + y = 60
Subtract 42 from both sides to find y:
y = 18
Therefore, the two numbers are 42 and 18.