college problem solving

posted by .

a certain two-digit number is 6 less than the sum of its tens digit and 7 times its units digit. if the digits are reversed the number is increase by 27. fin the original two-digit numbers

• college problem solving -

let the tens digit be x and the unit digit be y

then the number is 10x + y

10x+y = (x+7y) - 6
9x - 6y = -6
3x - 2y = -2 , #1

the number reversed would be 10y + x

so 10y+x = 10x+y + 27
9x - 9y = -27
3x - 3y = -9 , #2

#1 - #2
y = 7
then from #1, x = 4

the number is 47

check:
reverse it --- 74
is 74 -47 = 27 , so far so good

what is the sum of its tens digit and 7 times its unit digit
4 + 7(7) = 53
is 53 greater than 47 by 6 ? YEAHHHH

Similar Questions

1. math

This is an SAT question of the day that I can't understand. The sum of the digits of a three-digit number is 12. If the hundreds digit is 3 times the tens digit and the tens digit is 1 over 2 the units digit, what is the tens digit …
2. Digit Problems

If the tens digit of a two-digit number is subtracted from the units digit, the difference is 8. The number with the digits reversed is 10 more than nine times the units digit of the original number. Find the number.
3. ALgebra...plz help

If the tens digit of a two-digit number is subtracted from the units digit, the difference is 8. The number with the digits reversed is 10 more than nine times the units digit of the original number. Find the number.
4. algebra

A number consists of two digits. The sum of twice the tens digit an 5 times the units digit is 19. If the digits are reversed, the new number is 54 less than the original number. Find the number
5. Math

The mystery number's tens digit is less than the ones digit. The tens digit is less than the tenths digit. The tens digit is even. Its ones digit divided by its tens digit is 5. The product of two of the digits is 6 It has two odd …
6. Math - Algebra

What is the linear equation that will represent the second statement in the following problem: "The sum of the digits of a three-digit number is 12. If the hundreds digit is replaced by the tens digit, the tens digit by the units digit, …
7. Algebra

In a two-digit number, the tens digit is two less than the units digit. If the digits are reversed, the sum of the reversed number and the original number is 154. Find the original number.
8. Algebra

In a two-digit number the units’ digit is 7 more than the tens’ digit. The number with digits reversed is three times as large as the sum of the original number and the two digits. Find the number.
9. Math

In a two digit number the tens digit is two less than the units digit.If the digits are reversed, the sum of the reversed and the original number of 154.Find the original number.