SOLUTION: This is a digit and coin word problem. I know how to do simpler digit and coin problems so the main thing I need help with is how to rewrite this as equations. A two digit number

Algebra ->  Expressions-with-variables -> SOLUTION: This is a digit and coin word problem. I know how to do simpler digit and coin problems so the main thing I need help with is how to rewrite this as equations. A two digit number       Log On


   



Question 1050747: This is a digit and coin word problem. I know how to do simpler digit and coin problems so the main thing I need help with is how to rewrite this as equations.
A two digit number is four times the sum of its digits. The ones digit is 4 more than the tens digit. Find the original number.

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
A two digit number is four times the sum of its digits.
The ones digit is 4 more than the tens digit.
Find the original number.
Every two-digit number is made up of the first digit,
which tells us how many ten, and a ones (or units) digit,
which tells how many ones.

For example, 
the two-digit number 64 has 6 tens and 4 ones and is 6(10)+4(1).
the two-digit number 37 has 3 tens and 7 ones and is 3(10)+7(1).


A two digit number is four times the sum of its digits.
The ones digit is 4 more than the tens digit.
Find the original number.
Let t = the tens digit
Let u = the ones digit
Then 
the number = 10t+u
the sum of the digits = t+u

A two digit number is four times the sum of its digits.
So 10t+u = 4(t+u)

The ones digit is 4 more than the tens digit.
So u = t+4

We have this system of two equations and two unknowns:

system%2810t%2Bu=4%28t%2Bu%29%2Cu=t%2B4%29

Solve by substitution.  You finish.

Edwin