Coffee Blends A customer in a coffee shop purchases a blend...

Coffee Blends A customer in a coffee shop purchases a blend of two coffees: Kenyan, costing $\$ 3.50$ a pound, and SriLankan, costing $\$ 5.60$ a pound. He buys 3 lb of the blend, which costs him $\$ 11.55 .$ How many pounds of each kind went into the mixture?

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Key Concepts

Mixture Problems

Mixture problems involve combining two or more components with different properties (such as cost, concentration, or quality) to achieve a final mixture with a specified property. These problems require understanding how each component contributes to the overall mixture and often involve using algebraic relationships to determine the proportions or amounts of each component needed.

Systems of Equations

Systems of equations are sets of simultaneous equations that are solved together to find the values of unknown variables. In the context of mixture problems, one equation typically represents the total amount of the mixture, while another represents the total cost or concentration. Solving these systems allows determination of the individual quantities of each component in the mixture.

Weighted Average

The concept of weighted average is used to calculate an overall average value that takes into account the relative amounts, or weights, of each component in a mixture. In mixture problems, the cost or concentration of the final blend is calculated by multiplying the cost or concentration of each component by its proportional amount, followed by summing those products. This understanding is crucial for determining the required proportions of each component to meet a specified target average.

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