SOLUTION: a number is 8 times the sum of its digits. the tens digits is 5 greater than the units digit. find the number. PLEASE HELP!!! the answer is 72, but i dont know how to get there.
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Question 136036This question is from textbook algebra: structure and method: book1
: a number is 8 times the sum of its digits. the tens digits is 5 greater than the units digit. find the number. PLEASE HELP!!! the answer is 72, but i dont know how to get there.
This question is from textbook algebra: structure and method: book1
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let x = 10's digit
Let y = units digit
then
10x + y = "a number"
:
Write an equation for each statement and simplify:
:
"a number is 8 times the sum of its digits."
10x + y = 8(x+y)
10x + y = 8x + 8y
10x - 8x = 8y - y
2x = 7y
:
:the tens digits is 5 greater than the units digit."
x = y + 5
:
find the number.
:
Substitute (y+5) for x in the equation; 2x = 7y; solve for y
2(y+5) = 7y
2y + 10 = 7y
10 = 7y - 2y
10 = 5y
y =
y = 2
:
We know x = y + 5, therefore:
x = 2 + 5
x = 7
:
a number = 72
:
Did this show you how to get there?
:
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