Question 883725: the sum of two numbers is 99. if twice the smaller number is subtracted from the larger number, the result is 15 find the two numbers Found 2 solutions by JulietG, DrBeeee:Answer by JulietG(1812) (Show Source):
You can put this solution on YOUR website! A + B = 99
A - 2B = 15
Use the second equation and add 2B to each side to get:
A = 2B + 15
Now substitute the value of A from that equation into the first equation:
A + B = 99
(2B + 15) + B = 99
Add
3B + 15 = 99
Subtract 15 from each side
3B = 84
Divide each side by 3
B = 28
If B is 28, then A is 99-28, or 71
You can put this solution on YOUR website! Let a = larger number
Let b = smaller number
Then we have
(1) a + b = 99 and
(2) a - 2*b = 15 or
(3) a = 15 + 2*b
Put a of (3) into (1) to get
(4) 15 + 2*b + b = 99 or
(5) 3*b = 99 - 15 or
(6) 3*b = 84 or
(7) b = 28
Then using (1) we get
(8) a + 28 = 99 or
(9) a = 71
Check the answer with (2).
Is (71 - 2*28 = 15)?
Is (71 - 56 = 15)?
Is (15 = 15)? Yes
Answer: The two numbers are 71 and 28.
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