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

Let me try this,

5 for $1 and apples at 4 for $1.He spent a total of $19.50 this statement clearly tells that for 0.5 he buys apple(So that quantity can be integer.

Lets go with options : 50 walnuts
10$ Remaining amount -- 9.5 so total apple he buys = 38

total items 50+38 =88 he sells 20 for 5$ mean 4 for 1$
.So he earns == 22 dollors Diffrence 22-19.5 == 2.5 -- Wrong Answer.

2nd options 45 walnuts, 9$ for walnuts
10.5$ for apple 42 apple. so total quantity == 87 if he sells 4 for 1$. 21.75 == Diffrence less than 3$.

3rd choice, 60 walnuts, 12$ for walnuts.
7.5$ for apple -- 30 apples. total 90 if he sells 4 for 1$. 22.5so diffrence == 3$.

4th choice, 80 walnuts, 16$ for walnuts
3.5 for apples 14 apples. 94 total. if sells at 4 per 1$. 23.5 diffrence greater than 3.

5th choice 55 walnuts 11 $ for walnuts.
8.5 for apples, 34 apples. 89 in total. if sells at 4 per 1$. 22.15 diffrence less than 3.

So correct choice is C.

Haven't seen too many like this, but given he pays 20cts per walnut and 25cts per apple and sells each at 25cts, he actually makes no profit/loss on the apples, and so they become irrelevant to determine his profit of $3 (as does his cost basis of $19.50, because there is only one possible way for him to profit exactly $3).

@5cts profit per walnut, just need to calculate 3/.05 = 60

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.
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[/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!

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