Two Numbers with a Sum of 30 and a Difference of 15

Define variables:
Let x = larger number and y = smaller number
Resulting system of equations:
x + y = Sum
x − y = Difference
Solve the system of equations for x (larger number):
x =  
Sum + Difference/2

Find x by substituting given Sum and Difference into equation for x and simplify:
x =  
30 + 15/2

x =  
45/2

x =  22.5
Solve the system of equations for y (smaller number):
y =  
Sum − Difference/2

Find y by substituting given Sum and Difference into equation for y and simplify:
y =  
30 − 15/2

y =  
15/2

y =  7.5
Therefore, the two Numbers are 22.5 and 7.5
Check Sum of the two Numbers:
11
22.5
7.5
30.0
22.5 + 7.5 = 30 (trailing zero and decimal point are dropped) ✓
Check Difference between the two Numbers:
112
22.5
7.5
15.0
22.5 − 7.5 = 15 (trailing zero and decimal point are dropped) ✓

The solution above and other related solutions were provided by the Find two Numbers given Sum and Difference Application.

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