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Question 672743: If a two digit number is decreased by 45, the original number will be reversed. The number is 5 less than 8 times the sum of its digits. What is the number? (According to the answer in my book; they are showing 10x and x and no x and y or t and u). I need to know how they are doing it with just x and 10x.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! let x = the 10's digit
let y = the units
then
10x+y = the original number
:
Write an equation for each statement; simplify:
:
"If a two digit number is decreased by 45, the original number will be reversed."
10x + y - 45 = 10y + x
10x - x = 10y -y + 45
9x = 9y + 45
Simplify, divide thru by 9
x = y + 5
:
" The number is 5 less than 8 times the sum of its digits."
10x + y = 8(x+y) - 5
10x + y = 8x + 8y - 5
10x - 8x = 8y - y - 5
2x = 7y - 5
Replace x with (y+5), from the 1st statment
2(y+5) = 7y - 5
2y + 10 = 7y - 5
Get everything positive here
10 + 5 = 7y - 2y
15 = 5y
y = 15/5
y = 3
then
x = 3 + 5
x = 8
:
83 = the original number
:
:
See if that checks out in the 1st statement
"If a two digit number is decreased by 45, the original number will be reversed.
83 - 45 = 38; confirms our solution
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