SOLUTION: There are four nunbers. The first is twenty less than the second, the third is one more than twice the first and the fourth is four more than the third. We also know that the sum o

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Question 23781: There are four nunbers. The first is twenty less than the second, the third is one more than twice the first and the fourth is four more than the third. We also know that the sum of the first and second equals the sum of the third and fourth numbers. Find the numbers.
Can you please help us to figure this out. We would like step by step instructions.
thank you.
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
First number = f
second number = s
Third = number = t
fourth number = n

f = s-20 ---------------> s-f=20
t = 1 + 2s-40 ----------> 2s-t=39
n = 5 + 2s-40 ----------> 2s-n=35

s-20+s = 2s-39+2s-35 (sum of all numbers) -------> -2s = -54

Hence s = 27 (second number)
(27)-f = 20 ---------> s-f=20
f=7 (first number)

2(27)-t=39 --------->2s-t=39
54-t=39
t=15 (third number)

2(27)-n=35 --------->2s-n=25
54-n=35
n=19 Fourth number

to check first number + second number = third number + fourth number
27+7 = 19+15
34=34

Hence, the four numbers are 27, 7, 15 and 19.
Paul.