SOLUTION: need help urgent! 1. The one's digit of a two-digit number is three more than twice the ten's digit. the sum of one-third the number and ten is the number itself. What is the nu

Question 204525: need help urgent!
1. The one's digit of a two-digit number is three more than twice the ten's digit. the sum of one-third the number and ten is the number itself. What is the number?
2. The one's digit of a 2-digit number is one more than twice the ten's digit. if the number is reversed, the resulting number is two more than twice the original number. What is the original number?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
1. The one's digit of a two-digit number is three more than twice the ten's digit.
the sum of one-third the number and ten is the number itself.
What is the number?
:
Let x = the 10's digit
Let y = the units
then
10x + y = the two digit number
:
Write an equation for each statement:
"1. The one's digit of a two-digit number is three more than twice the ten's digit."
y = 2x + 3
:
"the sum of one-third the number and ten is the number itself."
(10x+y) + 10 = 10x + y
Get rid of the denominator, multiply by 3, results:
10x + y + 3(10) = 3(10x + y)
10x + y + 30 = 30x + 3y
30 = 30x - 10x + 3y - y
30 = 20x + 2y
Substitute (2x+3) for y (from the 1st equation)
30 = 20x + 2(2x+3)
30 = 20x + 4x + 6
30 - 6 = 24x
24 = 24x
x = 1 is the 10's digit
Find y:
y = 2(1) + 3
y = 5
then
15 = the number
:
Check solution in the statement:
"the sum of one-third the number and ten is the number itself."
*15 + 10 = 15
:
:
Do this the same way:
2. The one's digit of a 2-digit number is one more than twice the ten's digit.
if the number is reversed,
the resulting number is two more than twice the original number.
What is the original number?
:
" The one's digit of a 2-digit number is one more than twice the ten's digit."
y = 2x + 1
:
"if the number is reversed, the resulting number is two more than twice the original number."
10y + x = 2(10x+y) + 2
10y + x = 20x + 2y + 2
10y - 2y = 20x - x + 2
8y = 19x + 2
Substitute (2x+1) for y
8(2x+1) = 19x + 2
16x + 8 = 19x + 2
8 - 2 = 19x - 16x
6 = 3x
x =
x = 2 is the 10's digit
find y
You should be able to complete this problem by using the 1st problem as an example

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