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The sum of the two numbers is 58 and one of them exceeds the other by 18. Find the greater number.
30
36
40
38
38
For two numbers with sum S and difference D, the greater number is (S+D)/2. Here, (58+18)/2=76/2=38.
Sum of two numbers is 58, and the difference between them is 18.
x+y=58, x−y=18
For two numbers with sum S and difference D, the greater number is (S+D)/2. Here, (58+18)/2=76/2=38.
Confusing the greater number formula with the smaller number formula (S−D)/2, which would result in 20.
Define the variables
Let the two numbers be x and y, where x is the greater number.
x>y
Set up the equations
From the problem statement, we have the sum x+y=58 and the difference x−y=18.
x+y=58,x−y=18
Solve for the greater number
Add the two equations: (x+y)+(x−y)=58+18, which simplifies to 2x=76.
2x=76
Final calculation
Divide by 2 to find the value of x.
x=276=38
D is correct because solving the system of equations x+y=58 and x−y=18 yields x=38 as the greater number.
This concept is foundational for 'Ages' and 'Average' problems where relative differences between quantities are given.
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