Problem Solving

simba12123 wrote:Seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight, seed mixture y is 25 percent ryegrass and 75 percent fescue. If a mixture of x and y contains 30 percent ryegrass. WHat percent of the weight of the mixture is x?


a. 10 %
b.33.3%
c.40%
d.50%
e.66.67%

qa is b


although the answer explanation is nice in the back of the og 11 book, I am looking for a faster and less algebraic approach. ANy help?

Mixture of 40% Ryegrass and 25% Ryegrass is 30% Ryegrass

If Mixture of 40% Ryegrass and 25% Ryegrass were (40+25)/2 = 32.5% Ryegrass then both would have been equal in quantity

But Since Mixture of 40% Ryegrass and 25% Ryegrass is 30% Ryegrass so it's more influenced by 25% Ryegrass and therefore

40------(40-30)=10-------30------(30-25)=5-------25
i.e. the ratio must be 10:5 = 2:1 = y : x

i.e. x = (1/3)*100 = 33.33%

Answer: Option B

A couple of ways to solve this problem:

Algebra:https://youtu.be/obHR1MewMhA
Balance Method:https://youtu.be/EkkOwiyrhhQ

simba12123 wrote:Seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight, seed mixture y is 25 percent ryegrass and 75 percent fescue. If a mixture of x and y contains 30 percent ryegrass. WHat percent of the weight of the mixture is x?


a. 10 %
b.33.3%
c.40%
d.50%
e.66.67%

qa is b


although the answer explanation is nice in the back of the og 11 book, I am looking for a faster and less algebraic approach. ANy help?

I know this is very old, but I saw it had been bumped up today by Danny. A quicker way to solve this is as follows:

(1) Notice that the resultant mixture is closer to the composition of Y than X, so you know there must be more of Y than X. Therefore, choices (D) and (E) can be eliminated right off the bat and ignored altogether.

(2) Test answer choice B by seeing what the composition of the resulting mixture would be if we added 1/3 of X to 2/3 of Y. In this case, B works and B is the correct answer. However, had the resulting mixture contained too much ryegrass, then we would have added too much of X, and thus the correct answer would have been A. If the resulting mixture would have contained too little ryegrass, then we would not have added enough X, and thus the correct answer would have been C.

Hence, it would be possible to come to a correct solution on this question merely by checking choice (B).