How many pounds of 60-cent coffee and 87-cent coffee must a dealer mix to produce 90 pounds of coffee to sell for 69 cents oer pound.

Question

How many pounds of 60-cent coffee and 87-cent coffee must a dealer mix to produce 90pounds of coffee to sell for 69 cents per pound?

Answer 1

I assume that the dealer has x pounds of 60-cent coffee and y pounds of 87-cent coffee. To mix these two coffees we have:

60 * x + 87 * y

 

The dealer now has a mixed 69-cent coffee. The question tells us the mixed coffee weighs 90 pounds.

69 * 90

 

These two expressions are equivalent.

A) 60x + 87y = 69 * 90

 

On the other hand, consider the following equation, given that the weight of the mixed coffee is 90 pounds.

B) x + y = 90

 

Solve A and B for x and y:

For equation B find x in terms of y:

C) x = 90 - y

 

Use equation C to plug x in equation A in order to find y.

60 (90 - y) + 87 y = 69 * 90 >>>> 5400 - 60y + 87y = 6210 >>>> 27y = 810 >>>> y = 30 (pounds of 60-cent coffee)

 

Given y = 30 as the result of the previous step, solve the equation B to find x.

x + 30 = 90 >>>> x = 60 (pounds of 87-cent coffee)