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 13?

Get the answer to your homework problem.

Try Numerade free for 7 days

Jared J.

Algebra

12 months ago

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#

Logan H.

asked • 12/05/17

It is basically asking for a value I do not know how to find. 

3 Answers By Expert Tutors

Remember that decimal is a positional number system.

Let the digits of the two-digit number be "ab"     [this is a*10+b]

"reverse the digits in a certain two digit number you decrease its value by 9"    means

"the sum of it digits is 11"    means

  ----------------    [elimination; add equations]

Now, use either equation [eq1] or [eq2] to find the value of b:

 ---------------------------------    [elimination; subtract equations]

Kenneth S. answered • 12/05/17

Expert Help in Algebra/Trig/(Pre)calculus to Guarantee Success in 2018

Suppose the 2-digit number consists of t as the tens position, u as the units position.

Then the value of this number is 10t+u.

If the digits are reversed, a different number is formed & its value must be 10u+t.

Now you have two equations: 10t+u = 10u+t + 9 (because "When you reverse the digits in a certain two digit number you decrease its value by 9").

So you have a system of two equations and two unknowns, which you can solve.

Postingan terbaru

LIHAT SEMUA