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A rabbit on a controlled diet is fed daily 300 grams of a

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Re: A rabbit on a controlled diet is fed daily 300 grams of a  [#permalink]

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New post 08 Jul 2016, 04:14
1
1
10 % of 300 = 30 gms
15% 0f 300 = 45 gms

using allegation
45- 38/ 38- 30

= 7/ 8
therefore x :y is in the ratio 7: 8

7/ 15 X 300 = 140 gms
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Re: A rabbit on a controlled diet is fed daily 300 grams of a  [#permalink]

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New post 20 Jul 2016, 04:23
1
If food X = 140 grams ---protein = 14 grams
Food Y = 160 grams -----protein = 24 grams
total = 38 grams

Therefore B
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Re: A rabbit on a controlled diet is fed daily 300 grams of a  [#permalink]

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New post 18 Oct 2016, 09:10
Mixture problem. Definitely something to know for the exam! Let's dive in...

We know x+y=300 grams

Equation should be the following:

(0.10)x+(300-x)(0.15) = (0.1267)(300)

Solve for x. We get x = 140.
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Re: A rabbit on a controlled diet is fed daily 300 grams of a  [#permalink]

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New post 04 Jul 2017, 15:03
Success2015 wrote:
we can solve by testing answers
lets start with B...
let qty of X be 140 gms. so Y will be 160 gms.
proteins from X = 14 gms
proteins from Y = 24 gms
add both, we get 38gms.

so X must be 140 gms.


...That's what I did as well. That's the easiest and fastest way for me. Started with a middle term, got 37.5, but the question says EXACTLY 38 grams. So you need to decrease the amount of Food X since it has less protein to up the total. Hence, the answer is 140.
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A rabbit on a controlled diet is fed daily 300 grams of a  [#permalink]

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New post 29 Jan 2018, 23:23
Solved it by using the scale method (scale should be always of the same variable, here it is protein).

Protein in X ----- Avg Protein after mixing --------- Protein in Y

Based on above the scale becomes as below:

(Soln X) 10-----<\(\frac{38}{3}\)-10>-------\(\frac{38}{3}\)----<15-\(\frac{38}{3}\)>------15 (Soln Y)

\(\frac{X}{Y}\)=(15-\(\frac{38}{3}\))/(\(\frac{38}{3}\)-10)=\(\frac{7}{8}\)
To know X from the total mixture/solution= \(\frac{X}{X+Y}\)=\(\frac{7}{(7+8)}\)*300=\(\frac{7}{15}\)*300=140

Answer=(B)
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Re: A rabbit on a controlled diet is fed daily 300 grams of a  [#permalink]

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New post 31 Jan 2018, 16:14
tinman1412 wrote:
A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture.

A. 100
B. 140
C. 150
D. 160
E. 200


We can create two equations:

x + y = 300

y = 300 - x

and

0.1x + 0.15y = 38

Substituting, we have:

0.1x + 0.15(300 - x) = 38

0.1x + 45 - 0.15x = 38

7 = 0.05x

140 = x

Answer: B
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Re: A rabbit on a controlled diet is fed daily 300 grams of a  [#permalink]

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New post 31 Jan 2018, 19:20
tinman1412 wrote:
A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture.

A. 100
B. 140
C. 150
D. 160
E. 200


As per the given question -

\(3x + 3y = 900\)
\(2x + 3y = 760\)

\(x = 140.\)
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Re: A rabbit on a controlled diet is fed daily 300 grams of a  [#permalink]

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New post 20 Feb 2018, 11:52
tinman1412 wrote:
A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture.

A. 100
B. 140
C. 150
D. 160
E. 200




1.) x+y = 300 --> x = 300-y plug in the second equation

2.) .10x+.15y = 38

.10(300-y )+.15y = 38

y = 160 hence x is 140 :)

i will try another method 2morrow :)
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Re: A rabbit on a controlled diet is fed daily 300 grams of a &nbs [#permalink] 20 Feb 2018, 11:52

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