math
posted by Suzanne .
While adding ten twodigit numbers the digits of one of the numbers were interchanged. As a result the sum of all the ten numbers increased by a value which was four less than that number. Three times the sum of the digits of the original number is ten less than the number. What is the product of the digits of that number?
Please help how to obtain that number.

let the 10th digit be interchanged and in form 10x+y
therefore original sum
=> (a1+a2+...+a9) + 10x + y = S
but the sum obtained was::: (a1+a2+...+a9) + 10y + x = S' bcoz the digits were interchanged
"the sum of all the ten numbers increased by a value which was four less than that number"
therefore!!
S'  S = (10x+y)  4
the a1, a2...a9 gets cancelled out & what is left is
=> 9(yx)=10x+y4 => 8y19x=(4)...
"three times the sum of digits of that original number is ten less than the number"
therefore
=> 3(x+y) = 10x+y  10 => 2y7x = 10...
by (1) & (2), the y can be cancelled out by multiplying (2) with 4 & adding (1) & (2)
the result we get is
=> 9x = 36 => x=4
therefore by (2)
2y 7.4= 10 => y=9
therefore x.y = 36
Respond to this Question
Similar Questions

MATH Trouble
I have no idea what this problem means: For how many twodigit numbers if the ones digit larger than the tensdigit? 
math
You have 2 digits, 2 numbers, reverse digits and 54 if the difference and the sum of all is 10 I'm not clear what you're asking, could you clarify what the conditions are for us please? 
Number Sentence
In a 4digit number, the two greatest placevalue digits are 2. The sum of the ones and tens digits is 14. What numbers are possible? 
Math
Can someone please help me write this statement out in formula form. There should be two formulas. Question.... Three times the larger of two numbers is equal to four times the smaller. The sum of the numbers is 21. Find the numbers. … 
math
The sum of two numbers is 25. Twelve less than four times one of the numbers is 16 more than twice the other number. Find both numbers. 
Grade 8 Math
Can you write them in Mathematical/numbers form I'll solve them myself. i don't really get it though i have written the first one in mathematical for but i'm not sure if that's right. 1. When six is subtracted from five times a certain … 
math
Consider all threedigit numbers that are greater than the sum of the squares of their digits by exactly 543. What are the last three digits of the sum of these numbers? 
maths
Find the sum of all 3digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3. Details and assumptions The digit sum of a number is the sum of all its digits. For example, 1123 has … 
math
Consider all threedigit numbers that are greater than the sum of the squares of their digits by exactly 543. What are the last three digits of the sum of these numbers? 
Mystery number
I have nine digits. The digit in the tens place is the value of any number times zero. The value of one of the digits is 40,000. The value of the hundredthousands place is ten times the digit in the tenthousand place. The digit in …