SOLUTION: Hi A tin of cookies is 630g when 1/2 full and 855g when 7/9 full. How many kilograms of cookies can the tin hold when full. Thanks

Question 1199193: Hi
A tin of cookies is 630g when 1/2 full and 855g when 7/9 full. How many kilograms of cookies can the tin hold when full.
Thanks

Found 2 solutions by math_tutor2020, josgarithmetic:
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

When you mention something like "A tin of cookies is 630g", I'm assuming you mean the contents and the container itself combine to 630 grams.

c = weight of the container only
x = weight of all the cookies only when the container is full
weights are in grams

(1/2)x = container is half full
(1/2)x + c = 630

(7/9)x + c = 855

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We have this system of equations
(1/2)x + c = 630
(7/9)x + c = 855

I'll rearrange them to this
(7/9)x + c = 855
(1/2)x + c = 630

Subtract those equations straight down.
It allows us to solve for x.
(7/9)x - (1/2)x + c - c = 855 - 630
(7/9-1/2)x = 225
(14/18-9/18)x = 225
(5/18)x = 225
x = 225*(18/5)
x = 810
The container can hold at most 810 grams of cookies.
This ignores the weight of the empty container itself.

Divide by 1000 to convert from grams to kilograms
810 g = (810/1000) kg = 0.81 kg

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Answer: 0.81 kg

Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
(NOT the only way to handle this):
Points as (x,y) for x amount full, y mass of the gross contents as grams.
( 1/2, 630) and ( 7/9, 855 ).

-

The full container of cookies, at x=1, is y=1035 grams.
The empty container , at x=0, is 225 grams.
The amount of cookies in GRAMS that the container can hold is grams.
This is the same as for x=1.
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