Respuesta :
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 [tex]x.[/tex]
Let the quantity of brazil nuts be [tex]y.[/tex]
So, total pound of mixture of nuts:
[tex]x+y=36\\y=36-x\ \ \ .....(1)[/tex]
Now, the total price of mixture per pound:
[tex]7.20(x)+4.00(y)=5.69(36)[/tex]
[tex]7.2x+4y=204.84[/tex]
Substituting the value of [tex]y[/tex] from equation (1) we get:
[tex]7.2x+4(36-x)=204.84[/tex]
[tex]7.2x+144-4x=204.84[/tex]
[tex]3.2x+144=204.84[/tex]
Subtracting both sides by 144 we get:
[tex]3.2x=60.84[/tex]
Dividing both sides by 3.2 we get:
[tex]x=19.01.[/tex]
The quantity of cashews = 19.01 pound.
Now, substituting the value of [tex]x[/tex] in equation (1) we get:
[tex]y=36-x\\y=36-19.01\\y=16.99.[/tex]
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.
