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

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Intern
Joined: 30 Jan 2016
Posts: 3
Re: A rabbit on a controlled diet is fed daily 300 grams of a [#permalink]

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08 Jul 2016, 05:14
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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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Concentration: Strategy, General Management
Re: A rabbit on a controlled diet is fed daily 300 grams of a [#permalink]

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20 Jul 2016, 05:23
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KUDOS
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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18 Oct 2016, 10:10
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.
Intern
Joined: 10 Nov 2013
Posts: 20
Re: A rabbit on a controlled diet is fed daily 300 grams of a [#permalink]

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04 Jul 2017, 16:03
Success2015 wrote:
we can solve by testing answers
let qty of X be 140 gms. so Y will be 160 gms.
proteins from X = 14 gms
proteins from Y = 24 gms

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.
Intern
Joined: 03 Oct 2016
Posts: 8
A rabbit on a controlled diet is fed daily 300 grams of a [#permalink]

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30 Jan 2018, 00:23
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

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

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31 Jan 2018, 17:14
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

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Joined: 31 Jul 2017
Posts: 335
Location: Malaysia
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Re: A rabbit on a controlled diet is fed daily 300 grams of a [#permalink]

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31 Jan 2018, 20:20
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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Joined: 09 Mar 2016
Posts: 349
Re: A rabbit on a controlled diet is fed daily 300 grams of a [#permalink]

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20 Feb 2018, 12:52
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
Re: A rabbit on a controlled diet is fed daily 300 grams of a   [#permalink] 20 Feb 2018, 12:52

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