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Question 261748: The sum of two numbers is 10 less than three times the first number. Their difference is 5 less than twice the second number. Find each of the Numbers.
Answer by unlockmath(1688)   (Show Source):
You can put this solution on YOUR website! Hello,
"The sum of two numbers "is" 10 less than three times the first number. Their difference "is" 5 less than twice the second number."
Looks like a lot of confusing tangled words at first, right?
(Here's a hint: the word "is" in math word problems usually means "equals")
We can set up two equations using "x" for the first number and "y" for the second number. They will look like this:
x+y=3x-10
x-y=2y-5
Makes sense so far?
Now with the first equation we'll subtract 3x from both sides and the second equation subtract 2y from both sides to give us:
-2x+y=-10
x-3y=-5 Now, Multiply this equation by 2 to give us:
2x-6y=-10 Add this equation to:
-2x+y=-10 When we add these two equations it gives us:
-5y=-20 Divide both sides by -5
y=4
Now we can solve for x by plugging 4 into either original equation.
x+4=3x-10 Subtract 3x from both sides and subtract 3 from both sides to be:
-2x=-14 Divide -2 into both sides to be:
x=7
There we go! plug these answers into the original equations and it will work!
Make sense?
:-)
RJ
Check out a new book I wrote at:
www.math-unlock.com
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