A Collection of Marbles

SydneyRoverP6B

SydneyRoverP6B

Well-Known Member
Staff member
Six small marbles and four large marbles have a combined mass of 30 grams, whilst seven small marbles and two large marbles have a combined mass of 23 grams.

What is the mass of each marble size?

Ron.
 
Also depends on the material they are made of! :wink:
And which defenition of mass you want! :|
inertial mass, active gravitational mass and passive gravitational mass. :wink:
 
pilkie wrote,..
Also depends on the material they are made of!
And which defenition of mass you want!
inertial mass, active gravitational mass and passive gravitational mass
Click to expand...

Hello Pilkie,...lol... :LOL:

i like that one,..but seriously there is no guessing to me made, everything you need to know is given in the question.

Come on...give it a shot... :D

Ron.
 
SydneyRoverP6B said:
Six small marbles and four large marbles have a combined mass of 30 grams, whilst seven small marbles and two large marbles have a combined mass of 23 grams.

What is the mass of each marble size?

Ron.
Click to expand...

Right! S = small marble mass, L = Large marble mass

6S + 4L = 30 <=== 1
7S + 2L = 23 <=== 2

We can divide eqn 1 by 2, to get... 3S + 2L = 15 <=== 1'

eqn 2 - eqn 1' : (7S + 2L) - (3S + 2L) = (7S - 3S) + (2L - 2L) = 4S + 0L = 4S = 23 - 25 = 8

Therefore, S = 8/4 = 2 grams.

Substituting S=2 back into eqn 1', 3x2 + 2L = 15 = 6 + 2L, so L = (15 - 6)/2 = 9/2 = 4.5 grams!

To check!

from eqn 2, 7S + 2L = 23 = (7x2) + (2x4.5) = 14 + 9 = 23 <=== Checks out!


S = 2 grams, L = 4.5 grams
 
1/. 6S+4L = 30

and

2/. 7S + 2L =23

From 2/. doubled -

14S + 4L = 46, and from 1/.
6S + 4L = 30

so 8S = 16

Small = 2,

(6x2) +4L = 30

4L = 18

Large = 4.5

Works for me Tommy 8)

Darth got his thunder back :evil:
 
Hello Darth and Richard,

That was a nice and easy one wasn't it. Well done to you both... :D

I have a slightly harder one,..although you both might find it just as easy, or will someone else beat you to it...

Ron.
 
quattro said:
1/. 6S+4L = 30

and

2/. 7S + 2L =23

From 2/. doubled -

14S + 4L = 46, and from 1/.
6S + 4L = 30

so 8S = 16

Small = 2,

(6x2) +4L = 30

4L = 18

Large = 4.5

Works for me Tommy 8)

Darth got his thunder back :evil:
Click to expand...

Glad you come with the same answers as me! :p :D

6S+4L = 30 <=== 1

7S + 2L =23 <===2

Just to be different, and introduce top heavy fractions (which everyone loves! :p)

eqn 2' = eqn 2 - (7/6) eqn 1 = (7S + 2L) - (7/6) x (6S + 4L) = 23 - (7/6) x 30

= (7S + 2L) - (7S + (14/3) x L) = 23 - 210/6
= (7S - 7S) + (2L - (14/3) x L) = 23 - 35 = -12
= 0S + ([-8/3] x L) = - 12
L = (-12 x 3 /-8) = -36/-8 = 36/8 = 9/2 = 4.5

S = (23 - 9)/7 = 14/7 = 2
 
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