A coffee shop owner blends a gourmet brand of coffee with a cheaper brand. The gourmet coffee usually sells for $9.00 per pound. The cheaper brand sells for $3.00 per pound. How much of each type should be mixed in order to have 40 pounds of coffee that is worth $7.50 per pound?

30 pounds of $9 brand

10 pounds of $3 brand

Step-by-step explanation:

let x = $9 brand

let y = $3 brand

system of equations:

x + y = 40

9x + 3y = 40(7.5)

substitution method:  x = 40 - y

9(40 - y) + 3y = 300

360 - 9y + 3y = 300

360 - 6y = 300

-6y = -60

y = 10

so, x = 40 - 10 or 30

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