# The costs of rice of brand A and rice of brand B are \$8 / kg and \$4 / kg respectively. If x kg of rice of brand A and y kg of rice of brand B are mixed so that the cost of the mixture is \$5 / kg , find x : y . A. 1 : 2 B. 2 : 1 C. 1 : 3 D. 3 : 1

## Expert Answers Let us say we have 1kg of the mixture.

Assume in the mixture we have xkg of brand A. Then from brand B we have ((1-x)kg of rice.

According to the data given;

Cost of brand A in mixture `= x(8) = 8x`

Cost of brand B in mixture` = (1-x)(4) = 4(1-x)`

Total cost of 1kg of mixture `= 8x+4(1-x) = 4(1+x)`

But it is given that the cost of mixture is \$5 per kg.

`4(1+x) = 5`

`4x = 1`

`x = 0.25`

`1-x = 0.75`

So the ration of brand A to brand B is 0.25:0.75 = 1:3.

Correct answer is at option C.

Approved by eNotes Editorial Team

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