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The sum of the digits of a certain two-digit number is 7. Reversing its digits increases the number by 9. What is the number?

1 Answer
Jan 22, 2016

Answer:

b=4 a=3

#color(blue)("The first digit is 3 and the second 4 so the original number is 34")#

To be honest! It would be much quicker to solve by trial and error.

Explanation:

#color(magenta)("Building the equations")#

Let the first digit be #a#
Let the second digit be #b#

#color(blue)("The first condition")#

#a+b=7# ...............................(1)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("The Second condition")#

#color(green)("The first order value: ")#
#color(white)(xxxx)a# is a counting in tens. So actual value is #10xxa#
#color(white)(xxxx)b# is counting in units. So actual value is #1xxb#

#color(green)("The first Order Value" =10a+b)#...............................(2)
'-----------------------------------------------------------------------'
#color(purple)("The second order value:")#

#color(white)(xxxx)b# is a counting in tens. So actual value is #10xxb#
#color(white)(xxxx)a# is counting in units. So actual value is #1xxa#

#color(purple)("The second Order Value" =10b+a)#.........................(3)
'----------------------------------------------------------------------'

From the question
#color(red)("Equation (3)" - "Equation (2)"=9)#.................................(4)

#color(magenta)("|||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||")#

#color(blue)("Putting it all together")#

#"Equation 4 becomes" ->(10b+a) -(10a+b)=9#

#9b-9a=9 color(white)(..)............................................(4_a)#
#a+b=7 color(white)(..).................................................(1)#

From equation (1)
#a=7-b#

Substitute in #(4_a)# giving:
#9b-9(7-b)=9#

#9b+9b-63=9#

#18b=72#

#color(blue)(b=72/18 = 4)#

Substitute in Equation (1) giving
#a+b=7-> a+4=7#

#color(blue)(a=3)#