Question

How much coffee costing $4 a pound should be mixed with 3 pounds of coffee costing 4.50 a pound to obtain a mixture costing $4.30 a pound

Answer 1

The quantity of coffee costing $4 a pound in the coffee mixture is 2 pounds.

Explanation:

Given: Coffee costing $4 a pound is mixed with 3 pounds of coffee costing 4.50 a pound to obtain a mixture costing $4.30 a pound.

We have to find the quantity of coffee costing $4 a pound in the mixture.

Let x represent the number of pounds of $4 coffee.

Cost of one pound = 4x.

Cost of 3 pounds of coffee costing 4.50 a pound = 3(4.50)

Cost of mixture costing $4.30 a pound = (x+3)(4.30)

According to given problem,

`4x+3(4.50)=(x+3)4.30`

Solving for x, we get,

`\Rightarrow 4x+13.5=4.30x+12.9`

Rearranging like term together, we get,

`\Rightarrow 13.5-12.9=4.30x-4x`

`\Rightarrow 0.6=0.30x`

`\Rightarrow x=2`

Thus, the quantity of coffee costing $4 a pound in the coffee mixture is 2 pounds.