Hi

Is the answer is B ?

I tried with solution of putting the values.

SOLUTION

-->10% is too low to consider, so I ignored it.
-->then I checked it with 40% (being integer)

Create a matrix like below and compute only the value of Rye grass, as it is only related to our question.



33.33 will give the answer.

Then I discussed it with one of my friend, and he suggested me another solution but he is not sure about his solution. So you can test both method for such other question and select anyone you find easier.

2nd Method

Amount of Rye in X = 2/5
Amount of Rye in Y = 1/4
So in the mixture of XY, the value of Rye would be 2/5 * 1/4 = 1/10.
So, if percentage of Rye is 30 in the mixture then X = 33.33%

But I am not much sure about 2nd method, whether it will work for other problems or not, but it seems to be logically correct to me.

Enginpasa1 wrote:Is there an easier way to do this?
seed mixture X is 40% ryegrass and 60% bluegrass. Seed mixture Y is 25% ryegrass and 75% fescue. If a mixture of x and y contains 30% ryegrass, what percent of the weight of the mixture is X?

a.10%
b.33.33%
c.40%
d.50%
e.66.66 %


I am stumped

I am not very good at explaining questions over the net.. so bear with me.

This question is based on the concept of weighted average. Let me explain weighted average with an example.

Consider 2 classes. Class A has 3 students and Class B has 5 students. Suppose the average marks in English for class A is 60 and that for Class B is 80. What is the average marks in English for Class A and Class B combined ?. It is not 60 + 80 = 140 / 2 = 70 .. Why??, because the weights for the 2 marks are different. So the average in this case is (60*3+80*5 )/(3+5) = 72.5.

Suppose that Class A and Class B both had 4 students in that case what would be the average. It would be (60*4+80*4)/(4+4)=70, which is the same as (60 +80)/2 = 70, this is because both the marks have the same weight.

Using the same concept of weighted average in the above question . Take "a" liters of mixture X and "b" liters of mixture Y. So the new mixture created out of these 2 will be (a+b) liters in volume. Now the new mixture has 30% of ryegrass. This 30% is basically the weighted average of the ryegrass in the 2 mixtures X and Y mixed together in quantity "a"" and "b" respectively.

So we have (40*a+25*b)/(a+b)=30, solving this equation we have..

40a+25b=30a +30b, 10a=5b, therefore a/b=1/2, so a/(a+b)= 1/3, so the percentage of X in the new mixture is 33%.

There are many ways to solve this question, one way has already been illustrated in the above post by codesnooker. You can also solve this question by allegation, which if used can help solve such questions in a few seconds. My post is to basically explain the concept of weighted average. Hope this helps you.

Regards.

therefore a/b=1/2, so a/(a+b)= 1/3, so the percentage of X in the new mixture is 33%


I followed you totaly up until your last logical step. can you please explain how I deduce down to 1/3 or 33.33%? Awesome explanation by the way

how did you know to multiply 1/4 and 2/5 to get 1/10. I can see with that logic that you can then multiply with 30%. BUt how did you know to do that?

Enginpasa1 wrote:therefore a/b=1/2, so a/(a+b)= 1/3, so the percentage of X in the new mixture is 33%


I followed you totally up until your last logical step. can you please explain how I deduce down to 1/3 or 33.33%? Awesome explanation by the way

Glad you liked it..

"a/b" gives the ratio of quantities of mixture X and mixture Y in the new solution, but the question asks for the percentage of X in the total solution. So we need a/(a+b)=1/3 over here a+b= the total solution.

Take an example. Let a= 10 liters and b = 20 liters such that a/b=1/2 (Remember "a" is the quantity of X and "b" is the quantity of Y in the new solution). Now, we need the % of "a" (or X) in the total solution so that would be 10/30= 10/(10+20)= a/(a+b)= 1/3. Over here we are taking values for "a" & "b" but we can also do this directly with the ratio a/b = 1/2 and the answer would remain the same.

Suppose we had to find the % of b in the total solution it would be b/(a+b)=2/(1+2)=2/3. Does this clear your doubt.

your answers are the best