Coffee blend

Statement

A barista must prepare $30$ kg of a coffee blend to be sold at $14$ EUR/kg, mixing a premium grade at $18$ EUR/kg with a standard grade at $12$ EUR/kg. How many kg of each?

Solution

Unknown. $x=$ kg of the premium grade; then the standard grade is $30-x$.

Equation. The total value must match: $18x + 12(30-x) = 14\cdot 30 \implies 6x + 360 = 420 \implies x=\boxed{10}$ We need $10$ kg of premium and $20$ kg of standard. The “weighted mean” structure of this problem is the same as the sample mean we shall meet in statistics.

Connections

Topics: First-degree equations
Concepts: Equation · Weighted mean
Methods: Mixture problem
Skills: Modelling · Solving equations
Exercise type: Word problem