# 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 ,...

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

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### 2 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.*

The costs of rice of brand *A *and rice of brand *B *are $8 / kg and $4 / kg respectively. x kg of rice of brand A is mixed with y kg of rice of brand B. The cost of the mixture is $5 per kg.

The cost of x kg of rice of brand A is 8x and the cost of y kg of rice of brand B is 4y. The mixture of rice obtained is worth 5*(x +y)

8x + 4y = 5*(x +y)

8x + 4y = 5x + 5y

8x - 5x = 5y - 4y

3x = y

x/y = 1/3

The ratio x:y is 1:3