Question

A merchant has coffee worth $30 a pound that she wishes to mix with 80 pounds of coffee worth $90 a pound to get a mixture that she will sell for $70 a pound. How many pounds (lb) of the $30 coffee should be used?

Answer 1

To find the amount of coffee worth $30 a pound that should be used in the mixture, set up an equation based on the given information and solve for x.

Step-by-step explanation:

To find the amount of coffee worth $30 a pound that should be used, we can set up an equation based on the given information. Let x be the number of pounds of $30 coffee. The total value of the $30 coffee is 30x. The total value of the $90 coffee is 90 * 80. We can set up the equation 30x + 90 * 80 = (x + 80) * 70 to represent the total value of the mixture. Solving this equation will give us the value of x, which represents the number of pounds of $30 coffee that should be used.

30x + 7200 = 70x + 5600

Subtracting 30x from both sides, we get:

7200 = 40x + 5600

Subtracting 5600 from both sides, we get:

1600 = 40x

Dividing both sides by 40, we get:

x = 40

Answer 2

You need 40 pounds of the $30 coffee.

Step-by-step explanation:

You need to calculate a weighted average for the $30/pound coffee and $90/pound coffee and equalize it to $70:

`(x*30 + 80 pounds * 90)/(x+80) = 70`

`30x + 7200 = 70(x +80) = 70x + 5600`

`40x = 1600`

`x = 40`