Question

The difference between two integers is 5. If the reciprocal of the smaller is added to twice the reciprocal of the larger the result is23/66. Find the two integers.

Answer 1

The difference between two integers is 5. If the reciprocal of the smaller is added to twice the reciprocal of the larger the result is 23/66. Find the two integers.

Answer 2

so let's check 2 values "a" and "b"
a - b =5 # their difference is 5
so, if you were to solve for "a", what would "a" be from that equation?

Answer 3

b + 5 = a

Answer 4

right, now that we know a = b+5, let's use that in the 2nd equation
$$
a-b = 5\\
\cfrac{1}{a}+\cfrac{1}{a}+\cfrac{1}{b}=\cfrac{23}{66} \implies
\cfrac{2}{a}+\cfrac{1}{b}=\cfrac{23}{66}\\
\text{now we know that a = b+5}\\
\cfrac{2}{b+5}+\cfrac{1}{b}=\cfrac{23}{66}\\
\cfrac{2}{b+5}+\cfrac{1}{b}-\cfrac{23}{66}=0
$$

Answer 5

Let a be the smaller integer (a < b);

If b - a = 5, and 1/a + 2/b = 23/66

Solve for b: b = 5 + a

Substitute into the other equation (substitution method): 1/a + 2/(5 + a) = 23/66

Simplify: (a + 5)/a*(a + 5) + 2*a/a*(a + 5) = 23/66 ----> (3*a + 5)/a*(a + 5) = 23/66 ....

Answer 6

How do you make you replies so neat looking jdoe0001

Answer 7

using a \(\huge \color{red}{la}\color{#226633}{tex} \ \ \color{blue}{editor} \)

Answer 8

heeh

Answer 9

i am confused on how you get those numbers?

Answer 10

Quiet, you; we have bigger problems now.

What's this latex editor of which you speak?

Answer 11

the values come from "substituting" the "a" in the 1st equation, to the 2nd equation
FROM the "difference" equation, TO the "reciprocals" equation

Answer 12

@cblrtopas ohhh, any editor really, I happen to use this one, this site does mathML, using a js library which uses latex syntax, thus

Answer 13

Ok, so I can write something in Word equation editor and just copy paste is that correct?

Answer 14

Word equation doesn't use Latex syntax, afaik

Answer 15

I usually paste in this box, because the [equation] editor here is not-so-fast
but if you use say -> http://mathb.in/ that one works just fine

Answer 16

Can I maybe code directly into the text box using a backslash or something?

I don't care how fast it is.

Answer 17

so I use http://mathb.in/ also, to check for syntax
if you want to check the js library Latex support -> http://www.onemathematicalcat.org/MathJaxDocumentation/TeXSyntax.htm

Answer 18

sure, you can, is how I do it, I just happen to use a Latex editor with premade buttons ehheh, but yeah

Answer 19

Gimme an example of how to code fractions.

Answer 20

{5}over{5}

Answer 21

@dwighthdz so far I have
$$
\cfrac{2}{b+5}+\cfrac{1}{b}-\cfrac{23}{66}=0\\
\frac{132b+66b+330-23b^2-115b}{(b+5)(b)(66)} =0\implies \frac{-23b^2+83b+330}{66b^2+330b}=0
$$

Answer 22

@cblrtopas \cfrac{5}{10} -> \(\cfrac{5}{10}\)

Answer 23

@cblrtopas \huge \cfrac{5}{10} -> \(\huge \cfrac{5}{10}\)

Answer 24

you can try and preview all those at http://www.onemathematicalcat.org/MathJaxDocumentation/TeXSyntax.htm

at http://mathb.in/

Answer 25

shoot I need to dash :/

Answer 26

Aha let me try: \cfrac{(3x+2)}{(x^(2)+5)}

Answer 27

Hmmmm

Answer 28

im still baffled

Answer 29

It's a system of equations: two equations with two unknowns we set up the two equations for you. You have to slog through the algebra and determine what's a and b.

Answer 30

We even eliminated one of the variables for you (follow either my derivation or jdoe's and just simplify)

Answer 31

So find what is b from jdoe's neat post

Answer 32

okay ill try thank you.

Answer 33

Then you can use your answer to get a