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brilliants [131]
3 years ago
9

How do I set up the equation for this word problem? A takes 1/2 of the diamonds plus 1 from the table. B takes 2/3 of what remai

ns. C takes 2/3 of what remains plus 1. One diamond is left. How many diamonds had originally been on the table? Answer is 38 but I don't know how to set it up.
Mathematics
1 answer:
nalin [4]3 years ago
3 0

The first thief takes (1/2 x + 1) .  What remains ?   x - (1/2x + 1)

So the 2nd thief takes  2/3 of  [  x - (1/2x + 1) ]

   What remains ?    x - 2/3 [ x - (1/2x + 1) ]

So the 3rd thief takes    2/3 of  { x - 2/3 [ x - (1/2x + 1) ] }  and he takes 1 more .

   What remains ?    x - ( 2/3 { x - 2/3 [ x - (1/2x + 1) ] } + 1 )

And that whole ugly thing is equal to ' 1 ', so you can solve it for 'x'..

The whole problem from here on is an exercise in simplifying
an expression with a bunch of 'nested' parentheses in it.  
===============================================
This is a lot harder than just solving the problem with logic and
waving your hands in the air.  Here's how you would do that:

Start from the end and work backwards:

-- One diamond is left.
-- Before the 3rd thief took 1 more, there were 2.
-- That was 1/3 of what was there before the 3rd man took 2/3.
So he found 6 when he arrived.
-- 6 was 1/3 of what was there before the second thief helped himself.
So there were 18 when the 2nd man arrived.
-- 18 was 1 less than what was there before the first thief took 1 extra.
So he took his 1 extra from 19.
-- 19 was the remaining after the first man took 1/2 of all on the table.
So there were 38 on the table when he arrived.

Thank you for your generous 5 points.


 
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Find the domain of the function algebraically:<br><br> <img src="https://tex.z-dn.net/?f=R%28x%29%3D%5Cfrac%7Bx%7D%7Bx%5E%7B2%7D
BigorU [14]

The domain of the function is all real numbers except 2 and -1

Step-by-step explanation:

Domain is the set of inputs of a function on which the function is defined.

Given function is:

R(x) = \frac{x}{x^2-x-2}

In case of a function involving fraction, the function is undefined if the denominator is zero so in order to find the domain of the function algebraically , we have to find the values on which the function will be undefined

x^2-x-2 = 0\\x^2-2x+x-2 = 0\\x(x-2)+1(x-2) = 0\\(x+1)(x-2) = 0\\x+1 = 0 => x=-1\\x-2=0 = > x=2

The function will be undefined on x=-1 and x=2

So,

The domain of the function is all real numbers except 2 and -1

Keywords: Domain, functions

Learn more about domain and functions at:

  • brainly.com/question/2150928
  • brainly.com/question/2154850

#LearnwithBrainly

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3 years ago
A tendency to avoid putting money into high-risk investments is known as being _____.
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5 0
3 years ago
What is the equation 9x+6
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Step-by-step explanation:

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3 0
3 years ago
Conner has $3 more than Chi
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I think it’s 20 but I may be wrong
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The sum of two numbers is 5.036. one number has a 4 in the tenths place and 7 in the thousandths place. The other number has a 1
elena55 [62]
<span>Find the two numbers that has the sum of 5.036
First number has a 4 in the tenths place and 7 in the thousands
=> x.4x7
The other number has 1 in the ones place and 2 in the hundredths place
=> 1.x2x
=> x.4x7 + 1.x2x = 5.036
=> x.4x7 + 1.x2x = notice that the thousandths place is 7, add 9 to make it 16.
=> x.4x7 + 1.x26 = carry 1, then in hundredths place 2 + 1 + x, find the number to make it 3, since it’s already 3 x = 0
=> x.407 + 1.x29, in tenths place, notice that we already have 4, add 6 to make it 10, then carry 1 to ones place
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=> 3.407 + 1.629 = 5.036</span>



7 0
3 years ago
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