Puzzle:

A mixed packet of nuts contains 1 pound of walnuts and 2 pounds of Brazil nuts. It costs exactly $2. A packet containing 4 pounds of filberts and 1 pound of walnuts costs $3. And for only $1.50, you can buy a mixed packet of 3 pounds of almonds, 1 pound of walnuts, and 1 pound of filberts. How much should you pay for a mixture of 1 pound of each of the four kinds?

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Solution:

A mixture of 1 pound of each of the four kinds costs $2

A mixture of 1 pound of each of the four kinds costs $2

It is not possible to work out the cost per pound of each of the different nuts. However, the cost of various combinations can be worked out to get one pound of each of the four kind of nuts.

## 4 comments:

$2.....................rajesh

$2.

suppose

Walnuts = w

Brazil nuts = b

Filberts = f

Almonds = a

then equations would be.

1). w+2b = 2

2). w+4f = 3

3). w+f+3a = 1.5

or

3). w+f=1.5-3a

Now from eq 1 and 2

w+4(1.5-w-3a) = 3

w+6-4w-12a = 3

-3w-12a = -3

4). w+4a = 1

now eq 4- eq 1

4a-2b = -1

2a-b = -.5

b = 2a + .5

add b to the both side of eq 3

w+f+b = 1.5-3a+2a+.5

w+f+b+a = 2

As we can se for 1 pound of each of the four kind we ned to pay $2.

w+2b=2 .....(1)

4f+w=3.......(2)

3a+w+f=1.5...(3)

(1)+(2)+(3)= 3a+5f+3w+2b=6.5...(4)

(2)-(1)= 4f+2b=1

ie 2f=b+.5 ...(5)

put eqn 5 in eqn 4

ie 3a+3f+(b+.5)+3w+2b=6.5

3a+3f+3w+3b=6

a+f+w+b=2.

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