# Problem Solving Using Systems Of Equations 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.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.

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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.

The sum is 90: The larger number is 14 more than 3 times the smaller number: Plug into the first equation and solve: Then . Notice that you multiply the amount invested (the principal) by the interest rate (in percent) to get the amount of interest earned.

How many pounds of each kind of candy did he use in the mix?

The first and third columns give two equations: Multiply the first equation by 2 and subtract equations: Then He used 45 pounds of the \$2 candy and 5 pounds of the \$3.60 candy.

Suppose she uses x pounds of raisins and y pounds of dried fruit.

The first and third columns give the equations Multiply the second equation by 100 to clear the decimals. Suppose you have 50 pounds of an alloy which is silver.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.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.This gives Solve the equations by multiplying the first equation by 160 and subtracting it from the second: Hence, and . Then the number of pounds of (pure) silver in the 50 pounds is That is, the 50 pounds of alloy consists of 10 pounds of pure silver and pounds of other metals. Suppose you have 80 gallons of a solution which is acid.She needs 8 pounds of raisins and 9 pounds of nuts. Notice that you multiply the number of pounds of alloy by the percentage of silver to get the number of pounds of (pure) silver. Then the number of gallons of (pure) acid in the solution is So you can think of the 80 gallons of solution as being made of 16 gallons of pure acid and gallons of pure water.Phoebe wants to mix raisins worth

The first and third columns give the equations Multiply the second equation by 100 to clear the decimals. Suppose you have 50 pounds of an alloy which is silver.

The investor bought 120 shares of the \$35 stock and 240 shares of the \$45 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.

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.

This gives Solve the equations by multiplying the first equation by 160 and subtracting it from the second: Hence, and . Then the number of pounds of (pure) silver in the 50 pounds is That is, the 50 pounds of alloy consists of 10 pounds of pure silver and pounds of other metals. Suppose you have 80 gallons of a solution which is acid.

She needs 8 pounds of raisins and 9 pounds of nuts. Notice that you multiply the number of pounds of alloy by the percentage of silver to get the number of pounds of (pure) silver. Then the number of gallons of (pure) acid in the solution is So you can think of the 80 gallons of solution as being made of 16 gallons of pure acid and gallons of pure water.

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The first and third columns give the equations Multiply the second equation by 100 to clear the decimals. Suppose you have 50 pounds of an alloy which is silver.The investor bought 120 shares of the \$35 stock and 240 shares of the \$45 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.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.This gives Solve the equations by multiplying the first equation by 160 and subtracting it from the second: Hence, and . Then the number of pounds of (pure) silver in the 50 pounds is That is, the 50 pounds of alloy consists of 10 pounds of pure silver and pounds of other metals. Suppose you have 80 gallons of a solution which is acid.She needs 8 pounds of raisins and 9 pounds of nuts. Notice that you multiply the number of pounds of alloy by the percentage of silver to get the number of pounds of (pure) silver. Then the number of gallons of (pure) acid in the solution is So you can think of the 80 gallons of solution as being made of 16 gallons of pure acid and gallons of pure water.Phoebe wants to mix raisins worth \$1.60 per pounds with nuts worth \$2.45 per pound to make 17 pounds of a mixture worth \$2 per pound.How many pounds of raisins and how many pounds of nuts should she use?Let x be the number of shares of the \$35 stock and let y be the number of shares of the \$45 stock.The first and third columns give Multiply the first equation by 45, then subtract the second equation: Since , I have .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.This is where I get the headings on the tables below. There are twice as many nickels as pennies, so there are nickels. Be sure you understand 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. This might be the total cost of a number of tickets, the distance travelled by a car or a plane, the total interest earned by an investment, and so on.

.60 per pounds with nuts worth .45 per pound to make 17 pounds of a mixture worth per pound.How many pounds of raisins and how many pounds of nuts should she use?Let x be the number of shares of the stock and let y be the number of shares of the stock.The first and third columns give Multiply the first equation by 45, then subtract the second equation: Since , I have .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.This is where I get the headings on the tables below. There are twice as many nickels as pennies, so there are nickels. Be sure you understand 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. This might be the total cost of a number of tickets, the distance travelled by a car or a plane, the total interest earned by an investment, and so on.

## Comments Problem Solving Using Systems Of Equations

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