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aksik [14]
2 years ago
9

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

Mathematics
2 answers:
Elis [28]2 years ago
5 0
Let the two numbers be x and y.

According to your question;

x + y = 7
10y + x = 10x + y + 9

By equation 1 ; x = 7-y

Substituting the value of x ;

10y + ( 7 -y) = 10(7-y) + y + 9

9y + 7 = 70 -10y + y + 9

9y + 7 = 70 - 9y + 9

=> 18y = 70 -7 + 9
=> 18y = 72
=> y = 4

Substituting for x ;

x = 7 - y
=> x = 7 -4
=> x = 3

Thus, x = 3 and y = 4;
=> The number is 34.
AleksandrR [38]2 years ago
3 0
The original number is <u>34 </u>.
The sum of its digits is (3 + 4) = 7 .
Reversing its digits makes it 43 . . . 9 more than 34.

How I did it:  (There must be a much more elegant mathematical method)

There are only 6 possibilities for the original number.
They are . . .

16
25
34
43
52
61 .

Instead of trying to dream up a sophisticated equation,
I decided it was faster and easier to just go down the list
and look for one that worked. 
The third one I tried worked.
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SpyIntel [72]

Let

x------> the number of multiple choice question

y------> the number of free response question

we know that

3x+8y=55 -----> equation A

x+y=15

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Substitute equation B in equation A

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5y=10

y=2

Find the value of x

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x=15-2=13

therefore

<u>the answer is</u>

the number of multiple choice question are 13

the number of free response question are 2

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3 years ago
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Mashutka [201]
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A. 3.4
seropon [69]
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Hope that helps!
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