Coin Combinations Systems of Equations. ©Evergreen Public Schools 20102 Practice Target Practice 4: Model with mathematics.

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Presentation transcript:

Coin Combinations Systems of Equations

©Evergreen Public Schools Practice Target Practice 4: Model with mathematics.

©Evergreen Public Schools Learning Target Systems of Equations Learning Targets A-REIb I can solve a system of equations. How do you solve a system of equations by graphing?

More Pennies & Nickels Suppose you had a box with 519 coins (nickels and pennies) worth $ How many nickels are in the box?

Suppose you had a box with a total of 519 pennies and nickels worth $ How many nickels would you have? Let’s write a system of equations. What quantities are we counting in the problem? – Number of coins – Value of coins

Suppose you had a box of pennies and dimes with 519 coins worth $ How many nickels would you have? Identify the variables. Number of coins – Let x = number of nickels – Let y = number of pennies Value of coins – Let 5x = value of nickels in cents – Let y = value of pennies in cents Let’s write a system of equations.

Suppose you had a box of pennies and dimes with 519 coins worth $ How many nickels would you have? Let’s solve by graphing Number of coins x + y = 519 Value of coins 5x + y = There is something wrong with one of the equations. Fix it!

Suppose you had a box of pennies and dimes with 519 coins worth $ How many nickels would you have? Let’s solve by graphing x + y = 519 5x + y = Answer the question

x + y = 519 5x + y = 1727 Work together as a team to combine the equations and add them to the graph. Then write a conjecture. A.Add both equations.B. Subtract the first equation from the second equation. C. Double the first equation and add it to the second equation. D. Double the second equation and subtract it from the first equation. E. Multiply the first equation by -5 and add it to the second equation. F. Double the first equation and add it to three times the second equation. G. Make up your own combination. H. Make up your own combination.

Confirm Confirm your conjecture with the Coins In a Box problem you started with.