SOLUTION: A two digit counting number has a value that is 4 times the sum of its digits. If 4 times the units digit is 14 greater than the tens digit, what is the number?

Question 333631: A two digit counting number has a value that is 4 times the sum of its digits. If 4 times the units digit is 14 greater than the tens digit, what is the number?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A two digit counting number has a value that is 4 times the sum of its digits.
If 4 times the units digit is 14 greater than the tens digit, what is the number?
:
Let x = the 10's digit, and y = the units
10x+y is the number
:
"A two digit counting number has a value that is 4 times the sum of its digits."
10x + y = 4(x+y)
10x + y = 4x + 4y
10x - 4x = 4y - y
6x = 3y
simplify, divide by 3
2x = y
:
" If 4 times the units digit is 14 greater than the tens digit,"
4y = x + 14
:
We know y=2x, replace y in the above equation with 2x
4(2x) = x + 14
8x = x + 14
8x - x = 14
7x = 14
x = 2
then
y = 2(2)
y = 4:
:
what is the number?; 24 is the number
;
:
Check in the statement:
"4 times the units digit is 14 greater than the tens digit,"
4 * 4 = 14 + 2
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