Problem Solving Involving Linear Equation

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Phoebe has some 32-cent stamps, some 29-cent stamps, and some 3-cent stamps. Since the last two equations both involve y, I'll do everything in terms of y. I'll solve for x in terms of y: Plug and into and solve for y: Then Phoebe has 20 32-cent stamps, 10 29-cent stamps, and 5 3-cent stamps. The setup will give two equations, but I don't need to solve them using the whole equation approach as I did in other problems.

The number of 29-cent stamps is 10 less than the number of 32-cent stamps, while the number of 3-cent stamps is 5 less than the number of 29-cent stamps. Since one variable is already solved for in the second equation, I can just substitute for it in the first equation. The larger number is 14 more than 3 times the smaller number. Let L be the larger number and let S be the smaller number. At the end of one interest period, the interest you earn is You now have dollars in your account.

Such problems often require you to write two different linear equations in two variables.

Typically, one equation will relate the number of quantities (people or boxes) and the other equation will relate the values (price of tickets or number of items in the boxes).

The first and third columns give Multiply the first equation by 45, then subtract the second equation: Since , I have .

The investor bought 120 shares of the stock and 240 shares of the stock. I'll let x be the number of 32-cent stamps, let y be the number of 29-cent stamps, and let z be the number of 3-cent stamps. The last column says The number of 29-cent stamps is 10 less than the number of 32-cent stamps, so The number of 3-cent stamps is 5 less than the number of 29-cent stamps, so I want to get everything in terms of one variable, so I have to pick a variable to use.

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.

Suppose x of the .50 seats and y of the .50 seats were sold.

The first and third columns give the equations Multiply the second equation by 10 to clear decimals: Solve the equations by multiplying the first equation by 25 and subtracting it from the second: Then , so .

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