SOLUTION: The second of three numbers is 4 times the first number. The third number is 5 less than the second. If the first number is doubled and decreased by the third number, and the resul
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Question 653424: The second of three numbers is 4 times the first number. The third number is 5 less than the second. If the first number is doubled and decreased by the third number, and the result is the same as 23 more than the second number, what are the three numbers?
Answer by VirtualMathTutor(26) (Show Source): You can put this solution on YOUR website!
let f be first number
let s be second number
let t be third number
The second of three number is 4 times the first number:
s = 4f
The third number is 5 less than the second:
t = s - 5
If the first number is doubled and decreased by the third number and the result is the same as 23 more than the second number:
2f - t = 23 + s
Now that we have 3 equations, we can solve for f, s, and t:
Input t = s - 5 into the third equation:
2f - (s - 5) = 23 + s
Now replace every s with 4f
2f - (4f - 5) = 23 + 4f
Simplify
2f - 4f + 5 = 23 + 4f
-2f + 5 = 23 + 4f
subract 4f from both sides
-2f + 5 - 4f = 23
-6f + 5 = 23
subtract 5 from both sides
-6f = 18
divide both sides by -6:
f = -3
since s = 4f, then s = 4(-3) = -12
since t = s - 5, then t = -12 - 5 = -17
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