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Question 127730: The sum of two numbers is 6 less than twice the first number. Their difference is 10 less than four times the second number. Find each of the numbers
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Let x = one number
Let y = a second number
:
Write an equation for each statement;
(where you see the word "is", you can usually put an = sign):
:
"The sum of two numbers is 6 less than twice the first number.
x + y = 2x - 6
Simplify:
y = 2x - x - 6
y = x - 6
:
"Their difference is 10 less than four times the second number.
x - y = 4y - 10
Simplify
x = 4y + y - 10
x = 5y - 10
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Find each of the numbers
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Substitute (x-6) for y (from the 1st equation); find x:
x = 5(x-6) - 10
x = 5x - 30 - 10
x = 5x - 40
+40 = 5x - x
40 = 4x
x = +10
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Find y using the 1st equation
y = 10 - 6
y = 4
:
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Check solutions using the statement:
"Their difference is 10 less than four times the second number."
10 - 4 = 4(4) - 10
6 = 16 - 10; confirms our answer
:
How about this? Did it seem logical, and do you think you can handle these kind of problems now?
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