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Mixture A is 20% oil and 80% material B by weight. [#permalink]

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06 Aug 2013, 07:55

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Mixture A is 20% oil and 80% material B by weight. If 2 more kilograms of oil are added to the 8 kilograms mixture A, how many kilograms of mixture A must be added to make a 70% material B in the new mixture?

A)6 B)7 C)8 D)9 E)10

Can someone please explain the solution to this problem...

Re: Mixture A is 20% oil and 80% material B by weight. [#permalink]

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06 Aug 2013, 08:05

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To the 8 kg of solution A (which has \(0.2*8\) kg of oil), 2 kg of oil are added, so the resulting percentage of oil is:

\(\frac{0.2*8+2}{8+2}=\frac{3.6}{10}\), the resulting solution is 36% oil (3.6 kg) and 64% B (6.4 B). The \(x\) kg of mixture A that must be added to the new mixture, to obtain a 70% of B, is:

\(\frac{6.4 + 0.8x}{10+x}=0.7\), \(6.4+0.8x=7+0.7x\) so \(x=6\)

A

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Mixture A is 20% oil and 80% material B by weight. If 2 more kilograms of oil are added to the 8 kilograms mixture A, how many kilograms of mixture A must be added to make a 70% material B in the new mixture?

A)6 B)7 C)8 D)9 E)10

Can someone please explain the solution to this problem...

Old mix has 20% oil. You add 2 kgs of 100% oil. You get new mix with 30% oil (70% material B).

w1/w2 = (100 - 30)/(30 - 20) = 70/10 = 7/1 For every 7 parts of mix A, you have added 1 part of oil. Since you have added 2 kgs oil, mix A must be 7*2 = 14 kgs. You already had 8 kgs of mix A, so extra mix A added must be 14 - 8 = 6 kgs.

Re: Mixture A is 20% oil and 80% material B by weight. [#permalink]

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21 May 2016, 09:29

sva2300 wrote:

Mixture A is 20% oil and 80% material B by weight. If 2 more kilograms of oil are added to the 8 kilograms mixture A, how many kilograms of mixture A must be added to make a 70% material B in the new mixture?

A)6 B)7 C)8 D)9 E)10

Can someone please explain the solution to this problem...

Can be done with weighted avg method. if 2 kg more of oil is added to 20% oil of 8 kg mix,then a 10kg of mix will have 3.6kg (or 36%) of oil . A1=20(initial mix.) Avg. is what we need..ie 70% of material B means 30% of oil A2=36(36% of 10 kg mix) w1/w2=(A2-Avg)/(Avg-A1) (36-30)/(30-20) 6/10 means for every 10 kg of new mix. we need 6 kg of mix A Ans A

Mixture A is 20% oil and 80% material B by weight. [#permalink]

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21 May 2016, 10:22

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let a=kilograms of mixture a to be added to new mixture total oil in new mixture will be 1.6+2+.2a=3.6+.2a kilograms total weight of new mixture will be 8+2+a=10+a kilograms (3.6+.2a)/(10+a)=.3 a=6 kilograms

Last edited by gracie on 06 Nov 2016, 18:23, edited 1 time in total.

Mixture A is 20% oil and 80% material B by weight. If 2 more kilograms of oil are added to the 8 kilograms mixture A, how many kilograms of mixture A must be added to make a 70% material B in the new mixture?

A)6 B)7 C)8 D)9 E)10

Since mixture A is 8 kilograms by weight originally, it has 0.2(8) = 1.6 kilograms of oil and 0.8(8) = 6.4 kilograms of material B. After 2 more kilograms of oil are added, there will be 3.6 kilograms of oil but there will still be 6.4 kilograms of material B. Notice now we will have 10 kilograms of mixture A.

If we let x = the number of kilograms of mixture A to be added, we are adding 0.8x kilograms of material B, thus we have:

(6.4 + 0.8x)/(10 + x) = 0.7

6.4 + 0.8x = 7 + 0.7x

0.1x = 0.6

x = 6

Answer: A
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