MATH SOLVE

3 months ago

Q:
# 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

Accepted Solution

A:

Answer: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