Difficult Math Problem #119 - Arithmetic

X(0.4)+Y(0.25) = 0.3(X+Y)

0.1X = 0.05Y

Therefore 2X=Y

Total solution is X+Y and we want to calculate X/(X+Y) which is

X/(X+2X) = 1/3 so answer is B

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 this mixture is X ?

(A) 10%

(B) 33 1/3%

(C) 40%

(D) 50%

(E) 66 2/3%

4:6 (or 2:3) & 25:75 (or 1:3)

(40x/100+25y/100)/x+y = 30/100
Solving it gives us 10x=5y
or x/y=1/2
Thus answer should be B

OA:

(x+y)30/100 = x*40/100 + y*25/100
30x + 30y = 40x + 25y
y = 2x or y/x = 2/1 or y:x = 2:1 hence x = 33 1/3%

Let the weight of the mixture X be x
and the weight of the mixture Y be y

let r, b and f represent the weight of ryegrass,bluegrass and fescue respectively
In mixture X;
weight of r in X, i.e $$_{r_x}$$ = 40% of x = 0.4x
weight of b in X i.e $$_{b_x}$$ = 60% of x =0.6x

In mixture Y
weight of r in y i.e $$_{r_y}$$ = 25% of y =0.25y
weight of f in y, i.e $$_{f_y}$$ = 75% of y = 0.75%
In mixture of X and Y i.e x+y :
weight of r i n x + y i.e $$_{r_{x+y}}$$ = 30% of x+y = 0.3(x+y)
But $$_{r_{x+y}}$$ = $$_{r_x}$$ + $$_{r_y}$$
= 0.3(x+y)= 0.4x + 0.25y
0.3x+0.3y = 0.4x +0.25y
0.1x=0.05y
x=0.5y
Thertfoe percentage of x in x+y is
x $$_{\frac{x}{x+y}}$$ * 100% = $$_{\frac{0.5y}{0.5y+y}}$$ * 100%
Therefore the % of in x+y is $$_{\frac{0.5y}{1.5y}}$$ * 100% = 33.1/3%

Let the weight of the mixture X be x
and the weight of the mixture Y be y

let r, b and f represent the weight of ryegrass,bluegrass and fescue respectively
In mixture X;
weight of r in X, i.e $$_{r_x}$$ = 40% of x = 0.4x
weight of b in X i.e $$_{b_x}$$ = 60% of x =0.6x

In mixture Y
weight of r in y i.e $$_{r_y}$$ = 25% of y =0.25y
weight of f in y, i.e $$_{f_y}$$ = 75% of y = 0.75%
In mixture of X and Y i.e x+y :
weight of r i n x + y i.e $$_{r_{x+y}}$$ = 30% of x+y = 0.3(x+y)
But $$_{r_{x+y}}$$ = $$_{r_x}$$ + $$_{r_y}$$
= 0.3(x+y)= 0.4x + 0.25y
0.3x+0.3y = 0.4x +0.25y
0.1x=0.05y
x=0.5y
Thertfoe percentage of x in x+y is
x $$_{\frac{x}{x+y}}$$ * 100% = $$_{\frac{0.5y}{0.5y+y}}$$ * 100%
Therefore the % of in x+y is $$_{\frac{0.5y}{1.5y}}$$ * 100% = 33.1/3%