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
Inessa [10]
3 years ago
7

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?

Mathematics
2 answers:
stich3 [128]3 years ago
6 0
Let's say 'x' is the first digit in the number, and 'y' is the second one.
You already know that x + y = 7 .  Now here comes the fun part:

'x' is in the ten's place, so its value in the number is 10x , and the value
of the whole number is (10x + y).

If you flip the digits around, then 'y' is in the ten's place, its value is 10y ,
and the value of the whole new number becomes (10y + x) .

The problem tells you that when they're flipped around, the value is 9 more.

(10y + x) = (10x + y) + 9 more

10y + x = 10x + y + 9

Just to make it neater and easier to handle, let's subtract 1x and 1y from each side:

9y = 9x + 9

Now.  What to do with this.
Remember that one up at the top ... x + y = 7 ?  That's just what we need now.
Call it [ y = 7 - x ], and we can plug that into the one we're struggling with:

9y = 9x + 9

9(7 - x) = 9x + 9

63 - 9x = 9x + 9

Subtract 9 from each side:  54 - 9x = 9x

Add 9x to each side:    54 = 18x

Divide each side by 18:    3 = x

Great.    y = 7 - x      y = 4

The original number is  34 .    3 + 4 = 7
Flip the digits, and you have 43 .
43 is 9 more than 34 .
yay.
======================================

That was the <em><u>elegant</u></em> but tedious way to do it.
Here is the brute-force but easy way to do it:

List of all the 2-digit numbers whose digits add up to 7, and their flips :
16 . . . . . 61
25 . . . . . 52
34 . . . . . 43
43 . . . . . 34
52 . . . . . 25

Do you see a number that becomes 9 greater when you flip it ?

Right there in the middle of the list . . . 34 ==> 43 .


 


kondaur [170]3 years ago
3 0
10x+y-the\ number\\\\  \left\{\begin{array}{ccc}x+y=7\\10y+x=10x+y+9\end{array}\right
You might be interested in
What's the volume of this rectangular prism?
Snowcat [4.5K]

1. Find the length, width, and height of the rectangular prism.
2. Multiply the length, width, and height.
3. Write the answer in cubic units. For example: 60 inches3.

The length is the longest side of the flat surface of the rectangle on the top or bottom of the rectangular prism.

Ex: Length = 5 in.

<span>The width is the shorter side of the flat surface of the rectangle on the top or bottom of the rectangular prism. <span>Ex: Width = 4 in.The height is the part of the rectangular prism that rises up. Imagine that the height is what stretches up a flat rectangle until it becomes a three-dimensional shape. <span>Ex: Height = 3 in.You can multiply them in any order to get the same different result. The formula for finding the volume of a rectangular prism is the following: Volume = Length * Height * Width, or V = L * H * W. <span>Ex: V = 5 in. * 4 in. * 3 in. = 60 in.Since you're calculating volume, you're working in a three-dimensional space. Just take your answer and state it in cubic units. Whether you're working in feet, inches, or centimeters, you should state your answer in cubic units. <span>60 will become 60 in3.</span></span></span></span><span><span><span><span>
</span></span></span></span></span>


5 0
3 years ago
Read 2 more answers
What is 9+5x-5+3x? What could it be
qwelly [4]
8x+4 would be the answer if you combine like terms
6 0
2 years ago
Find the ratio of x to y is 5y=3x
Colt1911 [192]

Answer:

\frac{x}{y} = \frac{5}{3}

Step-by-step explanation:

given 5y = 3x ( divide both sides by 3 )

\frac{5}{3} y = x ( divide both sides by y )

\frac{5}{3} = \frac{x}{y}




5 0
3 years ago
Read 2 more answers
GENIUS OR ANYONE HELP ME PLZ PLZ PLZ!!!!
sukhopar [10]

Answer:

\frac{16}{4}, \frac{22}{7},\sqrt{5}, \sqrt{3}

Step-by-step explanation:

i got it right

8 0
2 years ago
Read 2 more answers
Solve the system of equations by graphing.<br> {y=x-6<br> {y=3x-8<br><br><br> Show work please
Zepler [3.9K]
You should subtract left sides and right sides in order to make y disappeared
and you will have the following:

y - y = (x - 6) - (3x - 8)    =>     0 = x - 6 - 3x - 8     =>     0 = -2x - 14    =>

2x = -14    =>    x = -14/2 = -7

Now you can use -7 in the system and you will get y
y = -7 - 6 = -13

So your answers will be:
x=-7 and y=-13


7 0
2 years ago
Other questions:
  • The equations of two lines are x - 3y = 6 and y = 3x + 2. determine if the lines are parallel, perpendicular or neither.parallel
    13·1 answer
  • A peach pie is divided into eight equal slices
    6·1 answer
  • Can someone please answer. There is one problem. There's a picture. Thank you!
    14·1 answer
  • I don't know the answer to this
    9·1 answer
  • A national survey of 2000 adult citizens of a nation found that 24​% dreaded​ Valentine's Day. The margin of error for the surve
    5·1 answer
  • PLEASE HELP MEEEEEE!!!!!<br> I literally have to get this done
    9·1 answer
  • The daily high temperature for the past two weeks in Orlando. ( 89, 90, 88, 91, 82, 90, 88, 88, 86, 90, 92, 87, 89, 86) Find the
    13·2 answers
  • Someone help me out with this my grade are bad
    12·1 answer
  • Image attached! Please help, and explain because I don’t understand!
    7·1 answer
  • Rotate shape A 90° clockwise with centre of rotation (0,0).
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!