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victus00 [196]
3 years ago
14

Two number differ by 3 The sum of their reciporcal is 7/10 find tge numbers

Mathematics
2 answers:
motikmotik3 years ago
6 0
The numbers are 5 and 2.

Reciprocals: 5- 5/10
                     2- 2/10
(2/10)+(5/10)= 7/10
5-2= 3
 
Answer: 5 and 2
Pachacha [2.7K]3 years ago
3 0
Comment
Let the larger number = x
Let the smaller number = y

Equations

x - y = 3                  (1)
1/x + 1/y = 7/10      (2)

Step one
solve for y
the common denominator on the left is xy So the left can be written as

\frac{y+x}{xy}

Then entire equation becomes

\frac{y+x}{xy}= \frac{7}{10}

Cross multiply
10*(x + y) = 7 * xy                         (3)

From the first equation x = 3 +y Put this into (3) 
10(3 + y + y) = 7*xy
10(3 + 2y) = 7xy               Make the same substitution on the right.10
10(3 + 2y) = 7(3 + y)*y
30 + 20y = 21y + 7y^2     Transfer the left side to the right side.
0 = 7y^2 + 21y - 20y - 30 
0=  7y^2 + y - 30              This will factor.

0 = (y - 2)(7y +15)

Step  Two
Solve for y    
y - 2 = 0
y = 2
or
7y + 15 = 0
7y = - 15
y = - 15/7
y = - 2.1428

Step Three
Solve for  x
If y = 2 then
x - y = 3
x - 2 = 3
x = 5

So one of the points is 
(5,2) Answer <<<<<<<<<<1st Answer

If y = - 2 1/7 then
x - - 2 1/7 = 3
x + 2 1/7 = 3    Subtract 2 1/7 from both sides.
x = 3 - (2 1/7)
x = 6/7

So the other point is (6/7, -2 1/7)  <<<< 2nd Answer
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Answer:

8:3

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Step-by-step explanation:

First, let's check if 9 and 24 have any common factor. If they do have any common ones, we must find the GCF (greatest common factor).

Factors of 9: 1, 3, 9

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

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1 < 3

Now that we know the GCF, we can divide the two numbers in the ratio 24 : 9 by it (3).

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24/3:9/3

<u>8:3</u>

Now that our ratio is simplified, it's going to be much easier to find more ratios that are equivalent. <u>8:3</u> is already one equivalent ratio, but if we multiply each number in the ratio by any other number, we can get a new equivalent ratio. Let's multiply each number in the ratio by 2:

<u>8:3</u>

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<u>16:6</u>

<u></u>

So, another equivalent ratio to 24:9 (and <u>8:3</u>) is <u>16:6</u>.

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