Question

The nutty professor sells cashews for 7.20 per pound snd brazil nuts flr 4.00 per pound. How much of each type should be used to make a 36 pound mixture that sells for 5.69 per pound?

Answer 1

Answer:

19.01 pound of cashews and 16.99 pounds of brazil nuts should be used to make a 36 pound mixture that sells for 5.69 per pound.

Step-by-step explanation:

Given:

The nutty professor sells cashews for 7.20 per pound and brazil nuts for 4.00 per pound.

Now, to find each type should be used to make a 36 pound mixture that sells for 5.69 per pound.

Let the quantity of cashews be $x.$

Let the quantity of brazil nuts be $y.$

So, total pound of mixture of nuts:

$x+y=36\\y=36-x\ \ \ .....(1)$

Now, the total price of mixture per pound:

$7.20(x)+4.00(y)=5.69(36)$

$7.2x+4y=204.84$

Substituting the value of $y$ from equation (1) we get:

$7.2x+4(36-x)=204.84$

$7.2x+144-4x=204.84$

$3.2x+144=204.84$

Subtracting both sides by 144 we get:

$3.2x=60.84$

Dividing both sides by 3.2 we get:

$x=19.01.$

The quantity of cashews = 19.01 pound.

Now, substituting the value of $x$ in equation (1) we get:

$y=36-x\\y=36-19.01\\y=16.99.$

The quantity of brazil nuts = 16.99 pounds.

Therefore, 19.01 pound of cashews and 16.99 pounds of brazil nuts should be used to make a 36 pound mixture that sells for 5.69 per pound.