Question

How many pounds each of dried fruit selling for $3.00 per pound and $3.80 per pound must be mixed to make a mixture of 80 pounds to sell at $3.50 per pound?

Answer 1

The quantity of dried fruit of $ 3 per pound is 30 pounds

The quantity of dried fruit of $ 3.80 per pound is 50 pounds .

Explanation:

Given as :

The price of one dried fruit = $ 3.00 per pound

The price of other dried fruit = $ 3.80 per pound

The total quantity of mix dried fruit = 80 pounds

The price of sell for mix dried fruit = $ 3.50 per pound

Let The quantity of dried fruit of $ 3 per pound = x pounds

And The quantity of dried fruit of $ 3.80 per pound = y pounds

Now , According to question

x + y = 80 pounds

And 3 × x + 3.8 × y = 3.5 × ( x + y )

Or, 3 x + 3.8 y = 3.5 x + 3.5 y

Or, 3.8 y - 3.5 y = 3.5 x - 3 x

or, 0.3 y = 0.5 x

Or, y =
`(0.5)/(0.3)` x

I.e y =
`(5)/(3)` x

Put the value of y in x + y = 80 pounds

I.e x = 80 - y

Or, x = 80 -
`(5)/(3)` x

Or, x +
`(5)/(3)` x = 80

or,
`(5 + 3)/(3)` x = 80

Or,
`(8)/(3)` x = 80

∴ x =
`(240)/(8)`

I.e x = 30

So,The quantity of dried fruit of $ 3 per pound = x = 30 pounds

Now, y = 80 - x

∴ y = 80 - 30

I.e y = 50

So,The quantity of dried fruit of $ 3.80 per pound = y = 50 pounds

Hence The quantity of dried fruit of $ 3 per pound is 30 pounds

And The quantity of dried fruit of $ 3.80 per pound is 50 pounds . Answer