Let us try to find a few more pairs of numbers from their sums and differences: (a) Sum = 27, Difference = 9 (b) Sum = 4, Difference = 12 (c) Sum = 0, Difference = 10 (d) Sum = 0, Difference = −10 (e) Sum = −7, Difference = −13
The two numbers are 18 and 9.
The two numbers are 8 and −4.
The two numbers are 5 and −5.
The two numbers are −5 and 5.
The two numbers are −10 and 3.
Explanation
(a) Using the formula: First number = (27 + 9)/2 = 18, Second number = (27 − 9)/2 = 9. Verification: 18 + 9 = 27 and 18 − 9 = 9. (b) Using the formula: First number = (4 + 12)/2 = 8, Second number = (4 − 12)/2 = −4. Verification: 8 + (−4) = 4 and 8 − (−4) = 12. (c) Using the formula: First number = (0 + 10)/2 = 5, Second number = (0 − 10)/2 = −5. Verification: 5 + (−5) = 0 and 5 − (−5) = 10. (d) Using the formula: First number = (0 + (−10))/2 = −5, Second number = (0 − (−10))/2 = 5. Verification: −5 + 5 = 0 and −5 − 5 = −10. (e) Using the formula: First number = (−7 + (−13))/2 = −10, Second number = (−7 − (−13))/2 = 3. Verification: −10 + 3 = −7 and −10 − 3 = −13.