SOLUTION: a number consist of two digit the difference of whose digit is 5 if 8 times the number equals to3 times the number obtained by reversing the digit find the number

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Question 1045477: a number consist of two digit the difference of whose digit is 5 if 8 times the number equals to3 times the number obtained by reversing the digit find the number
Found 3 solutions by josgarithmetic, MathTherapy, advanced_Learner:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
A number consists of two digits the difference of whose digits is 5. If 8 times the number equals to 3 times the number obtained by reversing the digits, find the number. 
t, tens place digit
u, ones place digit

system%28t-u=5%2C8%2810t%2Bu%29=3%28t%2B10u%29%29
If the solution does not work, then use u-t=5 and solve again.

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

a number consist of two digit the difference of whose digit is 5 if 8 times the number equals to3 times the number obtained by reversing the digit find the number
Since 8 times the ORIGINAL number equals 3 times the reversed number, it follows that the ORIGINAL number is smaller than the reversed number. Therefore T < U 

Original number: highlight_green%2827%29

Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
a number consists of two digit the difference of whose digit is 5 if 8 times the number equals to 3 times the number obtained by reversing the digit find the number
solution
x-y=5
let original number be 10y%2Bx
reverse number 10x%2By
8%2810y%2Bx%29=3%2810x%2By%29
80y%2B8x=30x%2B3y we know x=5%2By
80y%2B8%285%2By%29=30%285%2By%29%2B3%28y%29
80y%2B%2840%2B8y%29=%28150%2B30y%29%2B3%28y%29
88y%2B%2840%29=%28150%2B33y%29
88y-33y%2B%2840%29=%28150%29
88y-33y=%28150-40%29
55y=%28110%29
y=%28110%29%2F%2855%29
y=2
using y=2
x=5%2By
x=5%2B2
x=7
hence x=7,y=2
the number is 10y%2Bx
10%2A2%2B7
27
the reversed number
10x%2By
10%2A7%2B2
72
check
x is 7+ and y is 2
their difference is 7-2
5 check

the number 27
the reversed number 72
8* 27= 3*72
216= 216
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