SOLUTION: Define your variables, write a system of equations, solve and answer the question. One number is 4 less than a second number. Twice the second number is 38 more than 4 times th

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Question 1077896: Define your variables, write a system of equations, solve and answer the question.
One number is 4 less than a second number. Twice the second number is 38 more than 4 times the first. Find the two numbers.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
let a = one number
let b = a second numer
:
Write an equation for each statement
:
"One number is 4 less than a second number."
a = b - 4
Twice the second number is 38 more than 4 times the first.
2b = 4a + 38
From the 1st statement; replace a with (b-4)
2b = 4(b-4) + 38
distribute the 4
2b = 4b - 16 + 38
2b = 4b + 22
subtract 4b from both sides
2b - 4b = 22
-2b = 22
divide both sides by -2
b = 22/-2
b = -11 is the second number
then
a = -11 -4
a = -15 is the first number
:
:
Check this solution in the 2nd statement
" Twice the second number is 38 more than 4 times the first."
2(-11) = 4(-15) + 38
-22 = -60 + 38