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Name: _______________
Functions and Trig
Date: ______________
Activity 1.12 – Sam’s Cafe
In your job as buyer for Sam’s Café, a nationwide coffee bar, you need to buy
three grades of coffee bean that will be blended with various flavors to make
Sam’s well-known coffee drinks. This week the three grades of beans are selling
for $0.80, $1.20, and $1.80 per pound. You want to know how much of each grade
bean to buy, based on the following assumptions.
 The total weight of beans needed is 14,000 pounds
 Your budget is $14,800
 The weight of the least expensive grade must equal the total of the middle
grade weight and twice the most expensive grade weight.
Use x, y, and z to represent the different weights of each grade.
1. Write an equation for the total weight of the coffee beans.
2. Write and equation for the total cost.
3. Write an equation for the last of the three assumptions.
4. Write a 3X3 system of equations.
5. Solve the system to determine how much of each grade bean to buy
Name: _______________
Functions and Trig
Date: ______________
6. You are responsible for buying parts from a wholesale distributor. There are
three types of comparable switches that are needed. The cost per switch is
$1.20, $1.90, and $2.30. You need all three types and will place your order as
dictated by the following facts.
 You need a total of 12,000 switches in this order.
 Your budget will allow an expenditure of $23,400
 You need 3 times as many of the most expensive switches as the least
expensive switches.
7. Solve the following 3X3 linear system
x – 2y + z = -5
2x + y – z = 6
3x + 3y – z = 11