A person wishes to mix coffee worth $9 per lb with coffee worth $3 per lb to get 150 lb of a mixture worth $5 per lb. How many pounds of the $9 and the $3 coffees will be needed

50 lb of $9 coffee and 100 lb of $3 coffee

Step-by-step explanation:

Let x = the pounds of $9 coffee. Then

150 - x = the pounds of $3 coffee.

We can calculate the value of the coffee in each mixture.

x lb * $9/lb + (150 - x) lb * $3/lb = 150 lb * $5/lb

9x + 3 (150 - x) = 750

Distribute the 3 9x + 450 - 3x = 750

Combine like terms 450 + 6x = 750

Subtract 450 from each side 6x = 300

Divide each side by 6 x = 50 lb of $9 coffee

150 - x = 100 lb of $3 coffee

The person must mix 50 lb of $9/lb coffee with 100 lb of $3/lb coffee to get 150 lb of $5/lb coffee.

Check:

50 * 9 + 100 * 3 = 750

450 + 300 = 750

750 = 750