# Problem Solving Involving Linear Equation But they are convenient for organizing information --- and they give you a pattern to get started with problems of a given kind (e.g.interest problems, or time-speed-distance problems). In some cases, you the numbers in some of the columns in a table.

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Thus, 42 of the \$2.50 seats and 36 of the \$10.50 seats were sold. A total of 300 tickets are sold, and the total receipts were \$4140. The first and third columns give the equations Multiply the first equation by 15 and subtract equations: Then There were 120 tickets sold for \$12 each and 180 tickets sold for \$15 each.

An investor buys a total of 360 shares of two stocks.

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All of these different permutations of the above example work the same way: Take the general equation for the curve, plug in the given points, and solve the resulting system of equations for the values of the coefficients.

To review how this works, in the system above, I could multiply the first equation by 2 to get the y-numbers to match, then add the resulting equations: If I plug into , I can solve for y: In some cases, the whole equation method isn't necessary, because you can just do a substitution. The first few problems will involve items (coins, stamps, tickets) with different prices.

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If I have 6 tickets which cost each, the total cost is If I have 8 dimes, the total value is This is common sense, and is probably familiar to you from your experience with coins and buying things.

But notice that these examples tell me what the general equation should be: The number of items times the cost (or value) per item gives the total cost (or value). The total value of the coins (880) is the value of the pennies will go in the third column.

## Comments Problem Solving Involving Linear Equation

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