Hal bought walnuts at 5 for $1 and apples at 4 for $1.

Hal bought walnuts at 5 for $1 and apples at 4 for $1. He spent a total of $19.50 . He sells both at 20 for $5 and as a result gains $3 .How many walnuts did Hal buy ?

A. 50
B. 45
C. 60
D. 80
E. 55

Method 1:

Number of Walnuts=W
Number of Apples = A

Given that, Hal bought walnuts at 5 for $1 and apples at 4 for $1 and he spent a total of $19.50

So, \(\frac{W}{5} + \frac{A}{4}=19.5\) .......(1)

Given that, Hal sells both at 20 for $5 and as a result gains $3

So, \((\frac{W}{20})*5 + (\frac{A}{20})*4 = 19.5 + 3\)

Or, \(\frac{W}{4} +\frac{A}{4}= 22.5\) .......(2)

Solving (1) & (2), we get number of walnuts W as 60.

Answer: (C)

Method 2:

Given that, Hal bought walnuts at 5 for $1 and apples at 4 for $1.
Hence, buying price of walnut = 20 cents; buying price of apple = 25 cents

Given that, Hal sells both at 20 for $5 and as a result gains $3
Selling price of walnut or apple= $5/20 = 25 cents

Since, buying and selling price of apple is same, the profit of $3 is made by selling only walnut.
Profit from selling 1 walnut = (25 - 20 )cents= 5 cents
Number of walnut sold to get $3 profit = ($3)/(5 cents) = 60

Answer: (C)

He buys walnuts at a price of 20 cents each and apples at a price of 25 cents each. He then sells both of them at 25 cent each. This means that the 3$ profit he made result only from the walnuts.
Hence:

Profit = 3 $ = 300 cents / 5 cents = 60.

He bought 60 walnuts. Answer C.

Just look at the cost price & selling price of apples. They are same; so no profit is booked by them

They can be ignored in equation formation (One variable less )

Cost price of 1 walnut \(= \frac{1}{5}\)

Sell price of 1 walnut\(= \frac{1}{4}\)

Profit on 1 walnut\(= \frac{1}{4} - \frac{1}{5} = \frac{1}{20}\)

Total profit earned = 3

So, no. of walnuts sold \(= \frac{3}{\frac{1}{20}} = 20 * 3 = 60\)

Answer = C

I don't think the question is clearly stated. "Hal bought walnuts at 5 for $1" is it sufficiently clear? what source is the question from? are you posting an official question?

Yes, the rate is given. It could be in terms of $/cents per walnut or no. of walnuts per dollar. There shouldn't be a problem here.

[/quote] Yes, the rate is given. It could be in terms of $/cents per walnut or no. of walnuts per dollar. There shouldn't be a problem here.[/quote]
it should be more clearly stated, "Hal bought 5 walnuts for $1", if you say "Hal bought walnuts at 5 for $1", is it correctly written in formal English? honestly I've never seen such an idiom.

Each walnut costs: 20 c
Each apple costs: 25 c

At the time of selling
Each item sells at: 500/20 --> 25 c
So, in a way, no profit is being earned on selling apples. CP=SP
So, the total profit of 300 c is being earned on selling walnuts.
Profit on each walnut= 25-20=5c
No. of walnuts=Total profit/ profit on each walnut=300/5=60

The word'both' is misleading in this question. It should have been 'each'

Posted from my mobile device

I answered this question in 2:09 using plug in numbers. It felt the easiest and most tangible. I began with 5/$1= 20 cents/walnut and 4/$1 = 25 cent apples. I then took the total of $19.50 and added the profit of $3 to it to get $22.50.

From there I began with answer choice C to see what answer I would get.
- 60 walnuts * 20 cents each is $12.
- I know he spent $19.50 so I took 19.5-12=7.5
- Then I used that $7.50 towards apples. 7.50/25. (Or in this case, for quick math, I did 4 per dollar so 4x7=28+2=30 (the extra +2 was for the 50 cents))
-60 walnuts + 30 apples is 90 total items and he sold those at 20/$5. 20 goes into 80 4 times very quickly ($20 earnings) and leaves us with 10, or half of the $5 earnings left over. Add 20+2.50 and that’s the right answer!

I was lucky that c worked. If I started getting funny or hard to work with numbers I would have tried an easier answer choice to start off. Also, if it wasn’t C, I would know how far off I was and would move to either A or E depending on where I landed.

Hope this makes sense!

Posted from my mobile device

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