Final Answer:
The system of equations yields x = 20.5 and y = 7.5, not integers. Option d (18, 10) meets both conditions: sum = 28 and difference = 13. Therefore the correct answer is option d.
Step-by-step explanation:
Let's denote the two numbers as x and y. From the problem, we know that the sum of the numbers is 28, so the equation is x + y = 28. Additionally, the difference between the numbers is 13, so the equation becomes x - y = 13. We now have a system of equations:
x + y = 28
x - y = 13
We can solve this system using the elimination or substitution method. Adding the two equations eliminates y, resulting in 2x = 41, which gives x = 20.5. Substituting this value into x + y = 28 gives us y = 28 - x = 28 - 20.5 = 7.5. However, the numbers should be integers, and 20.5 and 7.5 don’t satisfy the conditions. Moving on to the options, option d (18, 10) satisfies both conditions: 18 + 10 = 28 (sum) and 18 - 10 = 8 (difference). Therefore, the correct pair of numbers is 18 and 10.
This problem requires solving a system of linear equations to find two numbers satisfying specific conditions. Setting up the equations x + y = 28 and x - y = 13 based on the sum and difference constraints respectively gives us a system of equations. Solving these equations using the elimination or substitution method, we find that x = 20.5 and y = 7.5, which aren't integers and don’t fulfill the criteria. Upon checking the given options, option d (18, 10) aligns with both conditions: the sum of 18 + 10 equals 28, and their difference is 18 - 10 equals 8, meeting the requirements of the problem.
The correct numbers that satisfy the conditions of having a sum of 28 and a difference of 13 are 18 and 10, as per the solution derived from the system of equations. Option d represents this solution accurately, fulfilling both the sum and difference constraints. Therefore the correct answer is option d.