![]() So if you have 2p nickels, they re worth 2p 5 = 10p cents. If you have 5 nickels, they re worth 5 5 = 25 cents. If you have 4 nickels, they re worth 4 5 = 20 cents. If the words seem too abstract to grasp, try some examples: If you have 3 nickels, they re worth 3 5 = 15 cents. number of coins cents per coin = total value pennies p 1 = p nickels 2p 5 = 10p total 880 1ΔΆ Be sure you understand why the equations in the pennies and nickels rows are the way they are: The number of coins times the value per coin is the total value. ![]() There are twice as many nickels as pennies, so there are 2p nickels. If there are twice as many nickels as pennies, how many pennies does Calvin have? How many nickels? In this kind of problem, it s good to do everything in cents to avoid having to work with decimals. You ll see that the same idea is used to set up the tables for all of these examples: Figure out what you d do in a particular case, and the equation will say how to do this in general. This is where I get the headings on the tables below. 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). dime This is common sense, and is probably familiar to you from your experience with coins and buying things. If I have 6 tickets which cost $15 each, the total cost is If I have 8 dimes, the total value is y = 0 6 tickets 15 dollars ticket = 90 dollars. ![]() ![]() The first few problems will involve items (coins, stamps, tickets) with different prices. You ll see this happen in a few of the examples. 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: 4x+6y = 20 x 6y = 5 If I plug x = 5 into 2x+3y = 10, I can solve for y: 5x = 25 x = y = 10 3y = 0 In some cases, the whole equation method isn t necessary, because you can just do a substitution. In many of the examples below, I ll use the whole equation approach. 1 Word Problems Involving Systems of Linear Equations Many word problems will give rise to systems of equations that is, a pair of equations like this: 2x+3y = 10 x 6y = 5 You can solve a system of equations in various ways. ![]()
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