If we do so we decrease the first number by 18. So,
#10a+b-18=10b+a#
# or, 10a-a+b-10b=18#
# or, 9a-9b=18#
# or, 9 (a-b)=18#
# or, (a-b)=(18/9)#
# or, (a-b)=2#...... (2)
Solving equation (1) and (2)
#a+b=10#... (1)
#a-b=2#... (2)
In equation (2).
#a-b=2#
# or, a=2+b#
Substitute in equation (1).
#a+b=10#
# or, 2+b+b=10#
# or, 2+2b=10#
# or, 2 (1+b)=10#
# or, 1+b=(10/2)#
# or, 1+b=5#
#:.b=5-1=4#
Re substitute in equation (1)
#a+b=10#
# or, a+4=10#
#:.a=10-4=6#
The numbers are #4# and #6#
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Jared J.
Algebra
12 months ago
You can put this solution on YOUR website!
When you reverse the digits in a certain two digit number you decrease its value by 27. Find the number if the sum of its digits is 3? ... let ten's digit be x units digit be y .. x+y = 3.................1 .. 10y+x= 10x+y-27 9y-9x=-27 /9 y-x=-3...................2 add (1) & (2) 2y=-3+3 2y=0 y=0 So x = 3
The number is 30
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Keleigh C.
2 Answers By Expert Tutors
Remember that the decimal number system is a positional number system. For decimal, that means ones place, tens place, etc. Let the number be xy [note: x is a digit in tens place and y is another digit in ones place] Learn to translate the words into formulas: "When you reverse the digits in a certain two-digit number you increase its value by 45." means 10y + x = (10x + y) + 45 [eq1] "the sum of its digits is 11" means x + y = 11 [eq2} Now, solve (let's use substitution): 10y + x = (10x + y) + 45 [eq1]
10(11-x) + x = 10x + (11-x) + 45
110 - 10x + x = 10x + 11 - x + 45
Now, put that into either equation to find the value of y:
Well we could just "crunch"the numbers: