SOLUTION: The sum of two integers are 10. Three times one integer is 3 less than 8 times the other integer. Find the numbers. I have tried 3x + 8(10 - x) - 3=10, also 3(10 - x)+ 8x

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Question 275440: The sum of two integers are 10. Three times one integer is 3 less than 8 times the other integer. Find the numbers.
I have tried 3x + 8(10 - x) - 3=10, also 3(10 - x)+ 8x - 3, I've started out on x+y=10, so if one integer is x, the other has to be (10 - x), like x + (10 - x)=10, but no answer. It seems like an easy one, can you help?
Thank you,
Alex Vargas
avargas91702@hotmail.com
Found 4 solutions by mananth, ikleyn, greenestamps, josgarithmetic:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website!
The sum of two integers are 10. Three times one integer is 3 less than 8 times the other integer. Find the numbers.

Let the integer be x
Three times = 3x
other integer = 8*(10-x)
The difference is = 3
8*(10-x)-3x= 3
80-8x-3x=3
-11x=-77
x= -77/-11
x=7
the other number is 24

Answer by ikleyn(53748)   (Show Source):
You can put this solution on YOUR website!
.
The sum of two integers are 10. Three times one integer is 3 less than 8 times the other integer. Find the numbers.
I have tried 3x + 8(10 - x) - 3=10, also 3(10 - x)+ 8x - 3, I've started out on x+y=10, so if one integer is x,
the other has to be (10 - x), like x + (10 - x)=10, but no answer. It seems like an easy one, can you help?
~~~~~~~~~~~~~~~~~~~~~~~~

In his solution to this problem, @mananth gives the answer "x = 7. The other number is 24."

This statement is incorrect. The correct answer is "one number is 7, the other number is 3".

Answer by greenestamps(13327)   (Show Source):
You can put this solution on YOUR website!

You have a problem common among students first learning to solve problems using algebra: turning the given information into a correct algebraic equation.

You do, however, have a good start on another part of setting the problem up -- using the information that the sum of the two number is 10 to call the two numbers "x" and "10-x".

Now for converting "Three times one integer is 3 less than 8 times the other integer" into a correct equation....

"Three times one integer..."
you have that part okay:
Your equation to here is "3x..."

"... is"
That is your equals sign; think of it as saying "is equal to" instead of just "is"
Now your equation is "3x =..."

"...3 less than 8 times the other integer"
Here is where beginning algebra students make a very common error. They see the "3 less..." and they write "3-...". But "3 less than A" is "A - 3", not "3 - A". So

"x" is your "one number", so the other number is "10-x". Then "8 times the other number" is "8(10-x)", and finally "3 less than 8 times the other number" is "8(10-x)-3".

And now you have the complete equation:

"3x = 8(10-x)-3"

Now you can solve using basic algebraic operations.

And the numbers are x=7 and (10-x)=3

ANSWERS: 7 and 3

Answer by josgarithmetic(39792)   (Show Source):
You can put this solution on YOUR website!
Integers x and y

three times one of them is three less than eight the other

add correspondings,

means

First number, 7
Other number, 3

SOLUTION: The sum of two integers are 10. Three times one integer is 3 less than 8 times the other integer. Find the numbers. I have tried 3x + 8(10 - x) - 3=10, also 3(10 - x)+ 8x - 3,