SOLUTION: there are four numbers. the first is twenty less the second, the third is one more than twice the first and the forth is four more than the third. we also know that the sum of the

Question 124902: there are four numbers. the first is twenty less the second, the third is one more than twice the first and the forth is four more than the third. we also know that the sum of the second equals the sum of the third and fourth numbers. find the numbers.:
there are four numbers. the first is twenty less the second, the third is one more than twice the first and the forth is four more than the third. we also know that the sum of the second equals the sum of the third and fourth numbers. find the numbers.
this is a grade 8 algebra question so no calculators so i need to understand how to get the answer from start to finish step by step. THANKS THANKS THANKS

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Rewrote the problem slightly
:
there are four numbers. the first is twenty less the second, the third is one more than twice the first and the forth is four more than the third. we also know that the sum of the first and the second equals the sum of the third and fourth numbers. find the numbers.:
:
Let the numbers be: w, x , y, z; in that order
:
Write an equation for each phrase/statement
:
" the first is twenty less the second, "
w = x - 20
:
"the third is one more than twice the first"
y = 2w + 1
:
"and the forth is four more than the third."
z = y + 4
:
"sum of the second equals the sum of the third and fourth numbers."
w + x = y + z
:
find the numbers.:
Get everything in terms of x
w = (x-20)
and
y = 2w + 1
y = 2(x-20) + 1; substituted (x-20)for w
y = 2x - 40 + 1
y = (2x-39)
and
z = y + 4
z = (2x-39) + 4: substitute (2x-39)for y
z = (2x-35)
And
w + x = y + z
Substitute for w, y, and z; and solve for x
(x-20) + x = (2x-39) + (2x-35)
2x - 20 = 4x - 74
-20 + 74 = 4x - 2x
54 = 2x
x =
x = 27
:
Find the other number
w = 27 - 20
w = 7
:
y = 2(27) - 39
y = 54 - 39
y = 15
:
z = 2(27 - 35
z = 54 - 25
z = 19
:
Determine if w + x = y + z; to confirm our solutions
7 + 27 = 15 + 19
34 = 34

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