Seven airline passengers in economy class on the same flight...

Seven airline passengers in economy class on the same flight paid an average of $\$ 361$ per ticket. Because the tickets were purchased at different times and from different sources, the prices varied. The first five passengers paid $\$ 420, \$ 210, \$ 333, \$ 695$, and $\$ 485$. The sixth and seventh tickets were purchased by a couple who paid identical fares. What price did each of them pay?

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Key Concepts

Equal Unknown Quantities

When multiple unknown quantities are stated to be identical, representing them with the same variable simplifies the problem. This allows for easier formation and solution of the equation by reducing the number of distinct unknowns.

Arithmetic Mean

The arithmetic mean is calculated by adding all the values together and dividing by the number of values. This concept is crucial in problems that involve finding averages or comparing individual values to the overall average.

Total Sum Calculation

When the average and the number of items are known, the total sum of the values can be determined by multiplying the average by the number of items. This technique is essential in solving problems where some values are unknown.

Setting Up Equations

Many problems involve unknown variables that can be determined by forming an equation based on the total sum and the known values. Setting up and solving such equations is a fundamental skill in algebra.

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