Final answer:
The student was asked to find two numbers based on their sum and difference. Using a system of equations, it was determined that the two numbers are -69 and -45.
Step-by-step explanation:
Finding Two Numbers Based on Their Sum and Difference
To solve the problem where the sum of two numbers is −114 and one number is 24 less than the other, we can set up a system of equations. Let the first number be x and the second number be y. The problem gives us two pieces of information:
x + y = −114 (the sum of the numbers)
x = y − 24 (one number is 24 less than the other)
Now, substitute the second equation into the first:
y − 24 + y = −114
2y − 24 = −114
Add 24 to both sides: 2y = − 90
Divide both sides by 2: y = − 45
After finding that y = −45, we can substitute this value back into the second equation to find x:
x = − 45 − 24
x = −69
Therefore, the two numbers are −69 and −45.