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 brand B are mixed so that the cost of the mixtures is $5/kg, find x:y.

Question

anonymous · Answer

@phi

phi · Answer

normally they give us the total kg of the mixture they want

anonymous · Answer

but the question didn't state that and that's why i ask you.......

phi · Answer

we can say x+y=1

anonymous · Answer

why?

phi · Answer

1 is a convenient number.  when we are done, we can find the ratio of x to y, which is what the question is asking

anonymous · Answer

okay..

phi · Answer

another way to do it is say
cost :  8x + 4y= 5(x+y)
simplify,  and then solve for the ratio x/y

anonymous · Answer

Note that this is the sum of the prices with the relative amounts of each brand A and brand B rice. If you have any experience with chemistry, this is very similar to calculating the average atomic mass given all the isotopes of an element. Anyway, moving on we can set up an equation like this:$$\bf 8x+4y=5$$I have chosen 'x' to be the percentage of the amount brand A rice in the mixture and 'y' as the percentage of brand B rice in the mixutre. This also allows to say that:$$\bf x+y=1$$And now we have a sytem of equations. Solving for 'x' and 'y' through substitution we get:$$\bf \implies 8x+4(1-x)=5 \implies 4x+4=5 \implies x = \frac{ 1 }{ 4 }$$Hence:$$\bf y=1-\frac{1}{4}=\frac{3}{4}$$Therefore we have 25% of brand A rice and 75% of brand B rice. Therefore:$$\bf x:y=\frac{ x }{ y }=\frac{ 1/4 }{ 3/4 }=\frac{1}{3}$$

anonymous · Answer

@kryton1212

anonymous · Answer

seems @genius12 's method is faster and easier ........

phi · Answer

?

anonymous · Answer

thanks @genius12 , haha
@phi how to simplify?

phi · Answer

For the second way  (the first way is what genius posted... with all the details)
 8x + 4y= 5(x+y)
8x +4y = 5x + 5y
3x = 1y
x/y = 1/3

anonymous · Answer

@kryton1212 Note that @phi method is perfectly valid as well. As a matter of fact, I like it better than mine as all you do is re-arrange and solve for x/y without substitution.

anonymous · Answer

lol

anonymous · Answer

but the medal can only give one person.......