SOLUTION: the sum of two integers is ten. three times the larger integer is three less than eight times the smaller interger. Find the intergers. i know the answer is 3 and 7 but teacher wa

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Question 3346: the sum of two integers is ten. three times the larger integer is three less than eight times the smaller interger. Find the intergers. i know the answer is 3 and 7 but teacher wants the algebraic expression and solution worked out and i can't do that
Answer by drglass(89) (Show Source):
You can put this solution on YOUR website!
To solve problems like this start by giving names to the integers. Call the bigger integer x and the smaller one y. Now, the problem tells us that the sum of x and y is 10. We can write this mathematically as:

The problem also tells us that "three times the larger integer is three less then eight times the smaller integer." Let's break this up a little, three times the larger means three times x (x is the larger, right?). Next we are told that is three less than eight times the smaller. Well, eight times the smaller is and three less than is . The problem says is or, .

This gives us two equations:

and

If we subtract y from both sides of the first equation, we get

Now substitute x in the second equation with and we get

multiply 3 into the first part of the equation to get

add 3 to both sides to get

add 3y to both sides to get

finally, divide both sides by 11 to get .

Since we know , we know