SOLUTION: A certain two digit number has a value that is eight less than five times the sum of it's digits. The tens digit is 3 less than the units digit. Find the number. Please help me sol

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Question 551130: A certain two digit number has a value that is eight less than five times the sum of it's digits. The tens digit is 3 less than the units digit. Find the number. Please help me solve this!
Found 2 solutions by lwsshak3, mathstutor458:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
A certain two digit number has a value that is eight less than five times the sum of it's digits. The tens digit is 3 less than the units digit. Find the number.
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let t=ten's digit
let u=unit's digit
t=u-3
original 2-digit number=10t+u
..
10t+u=5(t+u)-8
10(u-3)+u=5t+5u-8
10u-30+u=5(u-3)+5u-8
10u-30+u=5u-15+5u-8
u=7
t=u-3=4
original 2-digit number=47

Answer by mathstutor458(57) About Me  (Show Source):
You can put this solution on YOUR website!
let the number = xy
two digit number has a value that is eight less than five times the sum of it's digits.
xy=5(x+y)-8
The tens digit is 3 less than the units digit.
x=y-3
take y=4,so x=4-3=1 (if y=3,x=0 so we will not take this combination)
xy=14
check xy=5(x+y)-8
=>14=5(1+4)-8
=>14=25-8
=>14=17 does not satisfies the equation
take y=5,so x=5-3=2
xy=25
check xy=5(x+y)-8
=>25=5(2+5)-8
=>25=35-8
=>25=27 does not satisfies the equation
take y=6,so x=6-3=6
xy=36
check xy=5(x+y)-8
=>36=5(3+6)-8
=>36=45-8
=>36=37 does not satisfies the equation
take y=7,so x=7-3=4
xy=47
check xy=5(x+y)-8
=>47=5(4+7)-8
=>47=55-8
=>47=47 satisfies the equation
so the original number is 47.