SOLUTION: The sum of a certain number and a second number is 24. the first number minus the second number is 40. Find the numbers.

Question 810207: The sum of a certain number and a second number is 24. the first number minus the second number is 40. Find the numbers.

Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let a = the first number
Let b = the second number
The problem statement gives us two equations
(1) a + b = 24 and
(2) a - b = 40
To solve add (1) and (2) to get
(3) (a + b) + (a-b) = 24 + 40 or
(4) a + b + a - b = 64 or
(5) 2a + 0 = 64 or
(6) 2a = 64
Now divide each side of (6) by 2 to get
(7) 2a/2 =64/2 or
(8) a = 32
Using (1) with a = 32 we get
(9) 32 + b = 24 or
(10) b = 24 - 32 or
(11) b = -8
Check with (2).
Is (a - b = 40)?
Is (32 -(-8) = 40)?
Is (32 + 8 = 40)?
Is (40 = 40)? Yes
Answer: The two numbers are 32 and -8.
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