SOLUTION: The sum of the digits of a two-digit numeral is 10. The number named by the numeral is 18 more than the number named when the digits are reversed. What is the original numeral?
Eq
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Question 873914: The sum of the digits of a two-digit numeral is 10. The number named by the numeral is 18 more than the number named when the digits are reversed. What is the original numeral?
Equation & answer please.. Thank You!
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= tens digit.
= ones/units digit.
One of the statements in the problem says that
= value of the two-digit numeral.
= value of the number named when the digits are reversed.
Another statement in the problem says that
is more than .
That can be written as the equation
.
Subtracting and from both sides we get
, which simplifies to
Then, dividing both sides by , we get
--->--->
Take the equation above, and written at the beginning,
we have the system ,
which we call "a system of linear equations."
We can solve it "by substitution,"
meaning that we take an expression that is equal to one variable from one equation,
and substitute that expression for the variable in the other equation.
Substituting for in , we get
-->-->-->-->-->-->
Now, we substitute the value found for in to find the value of :
-->--> .
So, with and , the two-digit numeral is .
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