A feed store sells two varieties of birdseed:

[khushbumerchant]

A feed store sells two varieties of birdseed: Brand A, which is 40% millet & 60% safflower; Brand B, which is 65% millet & 35% safflower. If a customer purchases a mix of two birdseed that is 50% millet, what % of the mix is Brand A?

Solution:

Method 1.
Let, Brand A = 0.4x (of millet) + 0.6x (of safflower) = x
& let, Brand B = 65 (of millet) + 35 (of safflower) = 100
Hence, Mix of A & B = 0.5(x+100) (of millet)

Therefore, (0.4x + 65) = 0.5(x+100)
(0.4x + 65) = 0.5x + 50
0.1x = 15
x = 150

Method 2.
Let, Brand A = 40 (of millet) + 60 (of safflower) = 100
& let, Brand B = 0.65x (of millet) + 0.35x (of safflower) = x
Hence, mix of A & B = 0.5 (100+x) (of millet)

Therefore, (40 + 0.65x) = 0.5 (100+x)
(40 + 0.65x) = 50 + 0.5x
0.15x = 10
x = 10/0.15
x = 1000/15

My Query: When Brand B is assumed as "x" than x = 1000/15. Why this difference? Did i do something wrong? As per me, whether Brand A is assumed "x" or Brand B is assumed "x", the value for "x" should be derived as same. What is wrong in my understanding here. Someone, please help me highlight it & understand it here.

Thanks in advance.

[georgepa]

Organize

• Let A have a total of 100 lbs (pick a smart number)


• Let B have a total of x lbs (pick an unknown var for total lbs of B)


• So total of mixture = 100 + x


• Need %A in final mixture = A/Total = 100 / (100+x)

Code: Select All Code

   |  A  |    B   | Mixture
-----------------------------------   
M  | 40  | 0.65x  |  0.5(100+x)
S  | 60  | 0.35x  |
-----------------------------------
T  | 100 |   x    |  100 + x


Setup Equations

• 40 + 0.65x = 0.5 ( 100 + x)


• => x = 200/3


• A/Total = 100 / (100 + 200/3)


• = 100 / (500/3)


• = 100 * 3 / 500


• = 3/5 = 0.6


• = 60%

[georgepa]

My Query: When Brand B is assumed as "x" than x = 1000/15. Why this difference? Did i do something wrong? As per me, whether Brand A is assumed "x" or Brand B is assumed "x", the value for "x" should be derived as same. What is wrong in my understanding here. Someone, please help me highlight it & understand it here.

Thanks in advance.

Your numbers are correct. Its the final calculation of A/(A+B) that matters.

Your Method 1:

• B = 100


• A = 0.4x + 0.6x


• 0.4x + 65 = 0.5(100+ x)


• => x = 150


• So, A = 0.4 (150) + 0.6 (150)


• => A = 60 + 90 = 150


• A/(A+B) = 150/ (100 + 150)


• => A/(A+B) = 150/250 = 15/25 = 3/5 = 0.6 = 60%

Your Method 2:

• A = 100


• (40 + 0.65x) = 0.5 (100+x)


• => x = 1000/15 = 200/3


• A+B = 100 + x


• => A+B = 100 + 200/3


• => A+B = 500/3


• A/(A+B) = 100/[500/3] = 100 * 3 / 500 = 3/5 = 0.6 = 60%

[georgepa]

Since this is just a ratio of A/(A+B), you can also answer this question if you find the ratio of A/B. i.e If you know A/B - you can find A/(A+B)

Let A/B = x

• => A = Bx


• => A/(A+B) = Bx / (Bx + B)


• => A/(A+B) = Bx/(B[x+1])


• => A/(A+B) = x/(x+1)

Note: B/(A+B) = 1/(x+1). Since A/(A+B) + B/(A+B) = 1

Now use the given ratios to find the value of A/B

• 40A + 65B = 50(A+B)


• => 40A + 65B = 50A + 50B


• => 65B - 50B = 50A - 40A


• => 15B = 10A


• => A/B = 15/10 = 3/2

So

• x/(x+1) = (3/2)/(3/2 + 1)


• = (3/2) / (5/2)


• = 3/5 = 0.6 = 60%

[RonPurewal]

georgepa, do you have a question for us here? Doesn't seem that way, but just checking.

[georgepa]

Nope - I was responding to the question the poster asked

[RonPurewal]

Ok, thanks.

To the original poster -- If you have any funther questions on this one, please ask. Thanks.