Question 138534: A negative number is 5 less than a second negative number. If the second number is multiplied by 2 less than the first, the product equals 8. Find the numbers.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A negative number is 5 less than a second negative number. If the second number is multiplied by 2 less than the first, the product equals 8. Find the numbers.
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Let x = "the negative 1st number"
Let y = "the negative 2nd number"
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Write an equation for each statement:
"A negative number is 5 less than a second negative number."
x = (y - 5)
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" If the second number is multiplied by 2 less than the first, the product equals 8."
y * (x-2) = 8
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Find the numbers.
Substitute (y-5) for x in the above equation:
y * ((y-5)-2) = 8
y * (y - 7) = 8
y^2 - 7y = 8
y - 7y - 8 = 0
Factors to:
(y-8)(y+1) = 0
y = -1 is the solution we want
:
Find x using the 1st equation, substitute -1 for y:
x = -1 - 5
x = -6
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Our two negative numbers are -6 and -1
:
:
Check solution in the statement:
"the second number is multiplied by 2 less than the first, the product equals 8.
-1 * (-6 -2) =
-1 * -8 = +8
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