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Need help in understanding a percentage problem.

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  1. Nov 21, 2016 #1
    1. The problem statement, all variables and given/known data
    A grocer sells items by mixing small stones into grains. He has 50 kg each of two varieties of rice. He mixes 7.5 kg of stones in all. For one kg of rice, he mixes 100 grams of stones in the first variety and the remaining in the other. Peter purchases 5 kg of rice of each variety from the grocer. Approximately, what is the actual percentage of grain that Peter has?

    2. Relevant equations


    3. The attempt at a solution
    Does this line mean that he mixes 7.5 kg into 100 kg of rice i.e 50 kg of 1st variety and 50 kg of second.
    I did not understand the above statement.
    What does it mean?

    Given Solution :

    107.5 grams of total quantity has 100 grams of actual grains.
    Peter purchases 5 kg of each type.
    Hence, actual grains in 10 g = 10 * 100/107.5 close to 93.
    So, the required percentage is 93.

    Even the given solution is not clear to me.
    Help please.
     
    Last edited: Nov 21, 2016
  2. jcsd
  3. Nov 21, 2016 #2
    I would contact your teacher. The wording is very confusing.
     
  4. Nov 21, 2016 #3
    See if it helps.

    Given Solution :

    107.5 grams of total quantity has 100 grams of actual grains.
    Peter purchases 5 kg of each type.
    Hence, actual grains in 10 g = 10 * 100/107.5 is approximately 93.
    So, the required percentage is 93.

    Even the given solution is not clear to me.
     
  5. Nov 21, 2016 #4

    haruspex

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    Suppose Peter had purchased 107.5g. How much rice would he have?
     
  6. Nov 21, 2016 #5
    107.5 g of rice of variety 1 or 2?
    I don't think I can answer your question as I did not understand the given problem in the first place.
     
    Last edited: Nov 21, 2016
  7. Nov 21, 2016 #6
    How 107.5 grams of total quantity has 100 grams of actual grains?
    What is total quantity here?
     
  8. Nov 21, 2016 #7

    haruspex

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    He purchased equal amounts of the two.
     
  9. Nov 21, 2016 #8

    haruspex

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    If he had thought he bought 107.5g of rice, he would actually have bought 100g of rice and the rest of stones.
     
  10. Nov 21, 2016 #9
    But how do you know that 107.5g of rice contains 100g of rice and 7.5g of stones?
     
  11. Nov 21, 2016 #10

    haruspex

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    Ah, yes... I do believe the given answer may be wrong, and I was headed down the same path.
    Let's start again.
    What total mass of each variety is apparently being offered for sale?
    Given that Peter thinks he is buying 5kg of each, what fraction of each offering is he buying?
     
  12. Nov 21, 2016 #11
    Peter purchases 5kg of rice of variety 1 and this 5kg contains 4.5kg of rice and 0.5kg of stones as for one kg of rice, grocer mixes 100 grams of stones in the first variety .
    To answer your question, it's 0.9 for variety 1 and i don't know what it is for the 2nd variety.

    What is "remaining" here?
     
  13. Nov 22, 2016 #12

    haruspex

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    No.
    We need to start by figuring out exactly what the two lots of rice look like before Peter buys.
    This means that for each 1000g of rice of the first variety he adds to it 100g of stones. There were initially 50kg of rice in that basket, so what exactly is in that basket now?
    Of the total of 7.5kg of stones, those that did not go into the first basket go into the second. So what is now in the second basket?
     
  14. Nov 22, 2016 #13
    In 1st basket, we have 55kg now and 52.5kg in 2nd basket.
     
  15. Nov 22, 2016 #14
    Ok , I guess now I got it .
    107.5g contains 53.75g rice of variety 1 and 53.75g of variety 2.
    53.75g rice of variety 1 contains 10*53.75/11g of rice and the remaining is stones.
    Similarly, 53.75g variety 2 rice contains 53.75*20/21g of rice.
    Addition of 10*53.75/11g and 53.75*20/21g gives approximately 100g(actual value=100.0541126g).
    Hence, in 10kg of rice purchased by Peter ,the percentage of actual grains is (1000/107.5)*100/10 = 93.023

    Hope , it's correct.
     
  16. Nov 22, 2016 #15

    haruspex

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    Yes.
     
  17. Nov 22, 2016 #16
    Thank you haruspex :)
     
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