Question 124902
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.:
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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
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"and the forth is four more than the third."
 z = y + 4
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"sum of the second equals the sum of the third and fourth numbers."
 w + x = y + z
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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 = {{{54/2}}}
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