Need help in understanding a percentage problem.

[Thiru07]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

He mixes 7.5 kg of stones in all.

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.

For one kg of rice, he mixes 100 grams of stones in the first variety and the remaining in the other.

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.

 

[Isaac0427]

Homework Statement

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?

Homework Equations

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?

Help please.

I would contact your teacher. The wording is very confusing.

 

[Thiru07]

I would contact your teacher. The wording is very confusing.

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.

 

[haruspex]

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.

Suppose Peter had purchased 107.5g. How much rice would he have?

 

[Thiru07]

Suppose Peter had purchased 107.5g. How much rice would he have?

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.

 

[Thiru07]

How 107.5 grams of total quantity has 100 grams of actual grains?
What is total quantity here?

 

[haruspex]

107.5 g of rice of variety 1 or 2

He purchased equal amounts of the two.

 

[haruspex]

How 107.5 grams of total quantity has 100 grams of actual grains?
What is total quantity here?

If he had thought he bought 107.5g of rice, he would actually have bought 100g of rice and the rest of stones.

 

[Thiru07]

If he had thought he bought 107.5g of rice, he would actually have bought 100g of rice and the rest of stones.

But how do you know that 107.5g of rice contains 100g of rice and 7.5g of stones?

 

[haruspex]

But how do you know that 107.5g of rice contains 100g of rice and 7.5g of stones?

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?

 

[Thiru07]

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?

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.

For one kg of rice, he mixes 100 grams of stones in the first variety and the remaining in the other.

What is "remaining" here?

 

[haruspex]

this 5kg contains 4.5kg of rice and 0.5kg of stones

No.
We need to start by figuring out exactly what the two lots of rice look like before Peter buys.

For one kg of rice, he mixes 100 grams of stones in the first variety

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?

and the remaining in the other.

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?

 

[Thiru07]

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?

In 1st basket, we have 55kg now and 52.5kg in 2nd basket.

 

[Thiru07]

If he had thought he bought 107.5g of rice, he would actually have bought 100g of rice and the rest of stones.

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.

 

[haruspex]

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.

Yes.

 

[Thiru07]

Yes.

Thank you haruspex :)