**Q:** A coffee merchant has two types of coffee beans, one selling for $3 per pound and the other for $5 per pound. The beans are to be mixed to provide 100 pounds of a mixture selling for $4.18 per pound. How much of each type of coffee bean should be used to form 100 pounds of the mixture?

**A:** Let x= the number of pounds of the $3 beans

Let y = the number of pounds of the $5 beans

You have two variables, so you need two equations:

*Equation 1*: x+y=100 (because the mixture has a total mass of 100 pounds)

*Equation 2*: 3x + 5y = (4.18)*100 (each quantity is cost per pound *number of pounds)

Isolate for x in Equation 1: x = 100-y, and substitute into Equation 2:

3(100-y) +5y = 418

300-3y+5y=418

2y = 118

y=59

x = 100-y

x=100-59

x=41

So you would need 59 pounds of $5 beans, and 41 pounds of $3 beans.

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