SOLUTION: I am homeschooled with the School of Tomorrow, and am struggling with solving word problems involving two-digit numerals. The question I am having difficulty with now is this: "The

Question 215408: I am homeschooled with the School of Tomorrow, and am struggling with solving word problems involving two-digit numerals. The question I am having difficulty with now is this: "The value of a two-digit number is twice as large as the sum of its digits. If the digits were reversed, the resulting number would be 9 less than 5 times the original number. Find the original number." Thank you for your help!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
"The value of a two-digit number is twice as large as the sum of its digits.
---
Equation #1:
10t+u = =2(t+u)
-------------------

If the digits were reversed, the resulting number would be 9 less than 5 times the original number.
Equation #2:
10u+t =5(10t+u)-9
-------------------------
Find the original number."
================================
Rearrange the two equations:
#1: 8t-u = 0
#2: 49t-5u = 9
----------------------
Then:
u = 8t
Substitute for "u" to solve for "t":
49t-5(8t) = 9
9t = 9
t = 1
---
Since u = 8t, u = 8
---------------------------
The original number is 18
====================================
Cheers,
Stan H.
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