1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
barxatty [35]
2 years ago
9

The sum of the dibits of a two digit number is 15. The number obtained by interchanging its digits exceeds the given number by 9

. Find the original number.
Mathematics
1 answer:
QveST [7]2 years ago
3 0

Answer:

  78

Step-by-step explanation:

Interchanging the digits of a 2-digit number changes the value by a multiple of 9. The multiple is the difference between the digits of the number.

So, we have two digits that add to 15, and have a difference of 9/9 = 1. Since you're familiar with your addition facts, you know that the two digits are 7 and 8. Since the number we're looking for is the smallest of the numbers you can make with those digits, ...

  the original number is 78.

_____

More formally, let t and o represent the tens and ones digits of the original number.

  t + o = 15 . . . . . . the sum of digits is 15

  (10o +t) - (10t +o) = 9 . . . . swapping digits increases the value by 9

The latter equation simplifies to ...

  9o -9t = 9 . . . . collect terms

  o - t = 1 . . . . . . divide by 9 . . . (note the difference of digits is 9/9=1)

Adding this to the first equation gives ...

  (t +o) +(o -t) = (15) +(1)

  2o = 16

  o = 8

  t = o -1 = 7

The tens digit is 7 and the ones digit is 8: 78.

You might be interested in
Kayla brought 80 packs of cat food to feed the cats outside.
Akimi4 [234]

Answer:

It's 24 packs of cat food

Step-by-step explanation:

You have to think of it as 30% of 80.

30      ?

----- = ----

100    80

Now you have to find out what is in the blank by doing 80 times 30 to find what that equals. That equals 2,400. Now you have to find what times a 100 gets you 2,400. You divide a 100 by 2,400 to get 24. There's your answer

5 0
3 years ago
Read 2 more answers
working together Jacob and Kayla can clan an attic in 4.24 hours. had she done it alone it would have taken Kayla nine hours. ho
Marizza181 [45]
That’s not enough information to say how long he could do it. He could go slower or faster than her but by how much if so. So it’s not enough info.
5 0
3 years ago
I need the know the answer in A B C because I’m confused
bulgar [2K]

Answer:

Step-by-step explanation:

a) edj

b) ed

c) i think ag

4 0
2 years ago
2) Subtract and simplify. 11 7\10 − 7 3\10 =
Free_Kalibri [48]

Answer:

4 2/5

Step-by-step explanation:

     11 7/10

-      7 3/10

----------------

      4 4/10

4 4/10 = 4 2/5

4 0
2 years ago
Can some one help me PLEASEEE
notka56 [123]
3 months, 96 plus 78x3 = 330 (78x3=234+96) 110X3=330 meaning it is 3 months
3 0
3 years ago
Read 2 more answers
Other questions:
  • Which set of steps shows the solution to the equation 3y = -9?
    5·2 answers
  • What are the coordinates of the new triangle
    10·1 answer
  • Can y’all help me please
    12·1 answer
  • Find the equation of the linear function represented by the table below in slope-intercept form.
    11·1 answer
  • Convert: <br><br> 3 1/2 into an improper fraction =
    9·1 answer
  • Its eitheir a or c b and d dont check out what is it image down below
    6·2 answers
  • Pls help! Will give brainliest answer!!
    11·1 answer
  • Marc is filling 1-cup containers with juice.
    9·1 answer
  • Select the correct answer.
    9·1 answer
  • 50 Points
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!