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

Answer:

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

Step-by-step explanation:

Given that coffee costing $4 a pound mixed with 3 pounds of coffee costing $4.50 a pound . we have to find the number of pounds of coffee mixed with 3 pounds of coffee costing $4.50 a pound to obtain a mixture costing $4.30 a pound.

Let x be the pounds of coffee mixed.

Cost of coffee of 3 pounds costing $4.50 a pound is 3(4.50)=$13.5

Total weight of mixture=x+3

The cost per pound of the mixture will be the total value of the coffee in the mixture divided by the total weight of the mixture which is 4x+13.5 divided by total weight 3 + x.

∴ A/Q the equation becomes

$\frac{4x+13.5}{3+x}=4.30$

⇒ 4x+13.5=4.30(3)+4.3x

⇒ 0.6=0.3x

⇒ x=2

Hence, 2 pounds of coffee costing $4 should be mixed with 3 pounds of coffee costing 4.50 a pound to obtain a mixture costing $4.30 a pound.