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

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.

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.