$ MONEY $

Algebra Level 1

If $80 is divided among three people so that the second person will have twice as much as the first, and the third person will have $5 less than the second, then how many dollars will the third person have?

$18 $34 $29 $17

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17 solutions

Ryan Redz
Jun 24, 2014

Let the first person have $x. Then, the second has $(2x) and the third has $(2x-5).

Hence according to the statement of the problem, we have

(x)+ (2x) + (2x - 5) = 80.

\Rightarrow x = 17.

So the third person will have 2x - 5 = 2(17) - 5 = $29.

Here's what I solved in my mind. First: 42.5 + Second, which is half as much as the First: 21.25 + Third, that is $5 less than Second is 16.25. 42.5+21.25+16.25=80. IDK what just happened lol

Charina Sespeñe - 5 years, 4 months ago

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Yeah i got d same

Mukul Mishra - 5 years, 3 months ago

I fail to understand. Teh first person has $x; the second peson has 2x, and the third person has 2x-5. My equation lookslike this: x+2x+2x-5=80 or 5x-5=80, 5x=75, x+15.

Td Segall - 5 years, 3 months ago

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You have to add five to both sides not subtract it.

Pat Jane - 5 years, 3 months ago

Let y y be the amount that the first person will have, then the second person will have 2 y 2y and the third person will have 2 y 5 2y-5 . Since the sum is 80 80 , we have

y + 2 y + 2 y 5 = 80 y+2y+2y-5=80 \implies 5 y = 85 5y=85 \implies y = 17 y=17

The third person will have

2 y 5 = 2 ( 17 ) 5 = 34 5 = 2y-5=2(17)-5=34-5= $ 29 \boxed{\$29}

Mohammad Khaza
Sep 5, 2017

suppose, 1st person will get=x $

so, 2nd person will get=2x$

& the 3rd person will get=(2x-5)$

now, x + 2 x + 2 x 5 = 80 x+2x+2x-5=80

or, 5 x = 85 5x=85

or, x = 17 x=17

so, the 3rd person will get= 2 × 17 5 = 29 2 \times 17 -5=29 $

Nathan Blanco
Jun 26, 2014

The easiest way is just to work backwards. I happened to start with 29, but with each solution, it's x+(x+5)+(x/2)= 80, using the formula for each answer until you find one that fufils the formula, which is 29

The point was a challenge.

Jake Maason - 6 years, 11 months ago

The same way i do buddy ^^

Michael Wu - 6 years, 11 months ago
Gia Hoàng Phạm
Sep 22, 2018

a $ + 2 a $ + ( 2 a 5 ) $ = ( 5 a 5 ) $ = 80 $ 5 a $ = 85 $ a $ = 17 $ a\$+2a\$+(2a-5)\$=(5a-5)\$=80\$ \implies 5a\$=85\$ \implies a\$=17\$

( 2 a 5 ) $ = ( 2 × 17 5 ) $ = ( 34 5 ) $ = 29 $ (2a-5)\$=(2 \times 17-5)\$=(34-5)\$=\boxed{\large{29\$}}

let A be the amount of money of the first person, B the second person and C the third person

from the problem,

B = 2A

C = B - 5 = 2A - 5

we know that

A + B + C = 80

A + 2A + (2A - 5) = 80

A + 2A + 2A - 5 = 80

5A = 85

A = 17

C = 2(17) - 5 = 34 - 5 = 29

Tristan McCrea
Mar 6, 2016

I guessed :)

Youssef Hassan F
Jan 11, 2016

the equation is :

x + 2x + (2x-5)=80

to make it easy we will make it a different equation by removing the - 5 to the other side like this :

x + 2x + 2x = 80 + 5 = 85

now we will make a ratio like this :

1st : 2nd : 3rd : sum(1st + 2nd + 3rd)

1 : 2 : 2 : 5

? : ? : ? : 85

and take the v.of one part like this :

85 / 5 = 17

now back to the original equation

17 + (17 * 2) + (17 * 2 - 5) = 17 + 34 + (34 - 5) = 17 + 34 + 29 = 80

so the third money equals 29

Here's what I solved in my mind. First: 42.5 + Second, which is half as much as the First: 21.25 + Third, that is $5 less than Second is 16.25. 42.5+21.25+16.25=80. IDK what just happened lol

Charina Sespeñe - 5 years, 4 months ago
Achille 'Gilles'
Nov 2, 2015

Thomas Wood
Dec 31, 2014

First guy's money is N. Second guy's money is W. Third guy's money is T

Firstly, the total money is 80, so are first equation is:

N + W + T = 80

The second has twice as much as the first, so are second equation is:

W = 2N

The third has 5 less than the second, so finally:

T = W - 5

So our three equations are:

N + W + T = 80

W = 2N

T = W - 5

We want to have only one letter in the first equation, so we need to eliminate two

W = 2N >> N = 0.5W

Now we can rewrite the first equation with only W's (the second man's money) by replacing the N and T with their equations (T= W - 5) and (N = 0.5W)

(0.5W) + W + (W - 5) = 80

2.5W - 5 = 80 (simplified)

2.5W = 85 (added 5 to each side)

W = 34 (divided each side by 2.5)

So the second man would get get $34, and we can use our third equation to help us find the amount the third man gets

T = W - 5

T = 34 - 5 (filled in known variables)

T = 29 (added)

So the third man got $29

Kabir Bagai
Jul 19, 2014

x+2x+2x-5=80 5x=85 x=17 2*17-5 29

Anup Nishad
Jul 9, 2014

a+b+c=80; 2a=b; b-5=c; b=34 so a=29

2a=b; if b=34, then a=17

Aljun Tusi - 6 years, 11 months ago

let 'x' be the money the first dude have then according to the question, x+( 2x ) + ( 2x-5 ) = 80 then, 5x = 85 therefore, x= 17 so the third dude must have (2x - 5) i.e, the third dude have rs 29 !!!

David Bass
Jun 26, 2014

You can solve this problem by plugging each answer choice into the equation
x +1.5( x +5)=80. The only answer choice that fits is 29.

Praveen Kumar
Jun 25, 2014

Lets first man share be X then the solution is as follous ,X+2X+(2X-5)=80 gives X=17 but here we wants third person share which is (2X-5)=(2*17-5)=29

Vibhu Agarwal
Jun 25, 2014

Let the first one has $x.... According to question, second one will have $2x... Then third one would have $[80-(x+2x)]... But given, third will have 2x-5... So 2x-5=80-(x+2x)... 2x-5=80-3x... 5x=85... x=17... third one: 2x-5 = 29

Jathu Shan
Jun 25, 2014

let: x be the first dude, y be the second dude z be the third dude

x+y+z=80 y=2x z=2x-5

therefore, x+2x+(2x-5)=80 x+2x+2x-5=80 5x-5=80 5x=85 x=17

z=2x-5 therefore by substituting 17 into x we get the answer z=2*17-5 z=34-5 z=$29

Now check if 17+34+29=80

z=$29

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