The tens digit of a two-digit positive integer is 2 more than three times the ones digit. If the digits are interchanged, the new number 13 less than half the given number. Find the given integer. (Hint: Let x = tens-place digit and y = ones-place digit, then 10x + y is the number.)
i think 82 is the answer.
unit digit: x
tens digit: y
the actual number: 10y + x
number reversed: 10x + y
"the new number 13 less than half the given number" ---> 10x+y < (1/2)(10y+x) by 13
so , take 13 away from the larger part to make them equal.
10x + y = (1/2)(10y+x) - 13
20x + 2y = 10y + x - 26
19x -8y = -26
also y = 3x + 2
19x - 8(3x+2) = -26
19x - 24x - 16 = -26
-5x = -10
x = 2 , then y = 3(2)+2 = 8
the original number is 82
check: number reversed = 28
half the given number = 41
is half the given number (41) less than the number reversed (28) by 13 ??
math - This is an SAT question of the day that I can't understand. The sum of ...
Math - Write a number that has a hundreds digit less than 7, a tens digit less ...
Math - How do you write a number that has a hundreds digit less than 7 , a tens ...
math - My thousands digit is twice my hundreds digit. The sum of my tens and ...
Math - The mystery number's tens digit is less than the ones digit. The tens ...
math - i am a 4 digit number.my thousands didgit is 4 less than my tens digit.my...
math - This is an SAT Question of the Day. The sum of the digits of a three-...
5th grade math - i am a number greater than 40,000 and less than 60,000 my ones ...
4th grade - i am a 5 digit number my tens digit is the sum of my hundreds digit ...
math - The hundreds digit is half the tens digit. The sum of the hundreds and ...