Question

A merchant has coffee worth $60 a pound that she wishes to mix with 50 pounds of coffee worth $90 a pound to get a mixture that is worth $70 a pound. how many pounds (lb) of the $60 coffee should be used?

Answer 1

Explanation:

Alright, lets gets started.

Suppose she mixes x pounds of coffee of $ 60 a pound.

So, the cost of that coffee =
`60x`

Merchant has 50 pounds of coffee worth $ 90 a pound, hence the cost of this second coffee =
`90*50=4500`

The mixture she get, is worth $ 70 and the weight of this mixture will be
`(x+50)`

So, the cost of mixture will be =
`70*(x+50)`

Addition of both coffees will be equal to the mixture, so

`60x + 4500 = 70(x+50)`

`60x + 4500 = 70x + 3500`

Subtracting 60 x in both sides

`4500=10x + 3500`

Subtracting 3500 in both sides

`10x = 1000`

Dividing 10 in both sides

x = 100 pounds

It means she needs to add 100 pounds of that coffee. : Answer

Hope it will help :)