# Thread: systems of linear equations

1. ## systems of linear equations

1. A coffee merchant has coffee beans that sell for $9 per pound and$12 per pound. The two types are to be mixed to create 100 lb of a mixture that will sell for $11.25 per pound. How much of each type of bean should be used in the mixture? 2. 2. Originally Posted by Patience 1. A coffee merchant has coffee beans that sell for$9 per pound and $12 per pound. The two types are to be mixed to create 100 lb of a mixture that will sell for$11.25 per pound. How much of each type of bean should be used in the mixture?

2.
Hello, Patience,

let x be the amount of the cheaper coffee
let y be the amount of the more expensive coffee

then you get a system of simultanous equations:

A: x + y = 100
B: 9x + 12y = 11.25 * 100

I don't know which method you use to solve this system but you should get the results:
x = 25 and y = 75

EB

3. x + y = 100....(i)
9x + 12y = 1125....(ii)

(i) --> x = 100-y

(ii) --> 9(100-y) + 12y = 1125

900 - 9y + 12y = 1125
3y = 225
y = 75

(i) --> x = 100-75

x =25