Question 1207292
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360 liters of paint is made by mixing 3 paints A, B and C. 
The ratio by amount of paint A to B is 3:2 and that of B to C is 1:2. 
Paint A costs 1800 per liter. Paint B costs 2400 per liter. Paint C costs 1275 per liter . 
(a) Find the amount of each paint in 360 liters of the mixture. 
(b) Find the amount of money needed to make one liter of the mixture.
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<pre>
To say that    "The ratio by amount of paint A to B is 3:2 and that of B to C is 1:2"  is the same
as to say that "The ratio by amount of paint A to B is 3:2 and that of C to B is 2:1". 


Let 2x be the amount of paint B in 360 liters of the mixture.

Then the amount of paint A is  {{{(3/2)*(2x)}}} = 3x liters,
and the amount of paint C is  2*(2x) = 4x.


So, the 360 liters of the mixture is made of 3 equal parts of A,
two equal parts of B and 4 equal parts of C. 

Or, in all, 360 liters of the mixture is made of 3+2+4 = 9 equal parts of A, B and C.
Thus each elementary part is 360/9 = 40 liters.


Hence, the 360 liters of the mixture paint is made of 3*40 = 120 L of paint A,
2*40 = 80 liters of paint B and 4*40 = 160 liters of paint C. 

       It completes question (a).



The total cost of 360 liters is then

    120*1800 + 80*2400 + 160*1275 = 512000

and the cost of one liter of the mixture is

    512000/360 = 1700.

       It completes question (b).
</pre>

Solved.


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I intently presented the solution at the level of arithmetic problem to avoid using equations,
since this logic and this reasoning is accessible to &nbsp;4-th grade young students, &nbsp;who just know 
addition, &nbsp;multiplication and division of integer numbers, &nbsp;but may not know equations yet.