SOLUTION: the tens place of a two digit number is one less than half of the ones place. three times the ones place is equal to 8 times the tens place. what is the number?

Algebra ->  Real-numbers -> SOLUTION: the tens place of a two digit number is one less than half of the ones place. three times the ones place is equal to 8 times the tens place. what is the number?      Log On


   

Question 536534: the tens place of a two digit number is one less than half of the ones place. three times the ones place is equal to 8 times the tens place. what is the number?
Answer by fcabanski(1391) About Me  (Show Source):
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Call the number xy. x is the tens place, y is the ones place.


Equation 1: x = 1/2y -1 (the tens place of a two digit number is one less than half of the ones place)


Equation 2: 8x=3y (three times the ones place is equal to 8 times the tens place)


Two unknowns can be solved with two equations. Set y in terms of x in equation two, then substitute that into equation 1.


3y=8x


Divide both sides by 3.


y=8/3x


x = 1/2(8/3x) - 1


x = 4/3 x - 1


Subtract x from both sides.


-1/3x = -1


Multiply both sides by -3.


x = 3


3y = 8(3) (From equation 2). Divide both sides by 3.


The number is 38

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