SOLUTION: 6. If twenty-seven is added to a two digit number, the original number will be reversed. The number is four more than three times the sum of its digits. What is the number? 10.

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: 6. If twenty-seven is added to a two digit number, the original number will be reversed. The number is four more than three times the sum of its digits. What is the number? 10.       Log On

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Question 766286: 6. If twenty-seven is added to a two digit number, the original number will be reversed. The number is four more than three times the sum of its digits. What is the number?
10. The tens digit of a two digit number is five less than three times the ones digit. The number is twenty less than nine times the sum of the digits. What is the number?
Answer by lwsshak3(11628) About Me  (Show Source):
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6. If twenty-seven is added to a two digit number, the original number will be reversed. The number is four more than three times the sum of its digits. What is the number?
let u=ones digit
let t=tens digit
27+10t+u=10u+t
10t+u=3(t+u)+4
..
27=-9t+9u
4=7t-2u
..
-18t+18u=54
63t-18u=36
add
45t=90
t=2
2u=7t-4=14-4=10
u=5
number: 25

10. The tens digit of a two digit number is five less than three times the ones digit. The number is twenty less than nine times the sum of the digits. What is the number?
t=3u-5
10t+u=9(t+u)-20
..
10(3u-5)+u=9(3u-5+u)-20
30u-50+u=36u-45-20
-5u=-15
u=3
t=3u-5=4
number: 43