Coin Combinations

Systems of Equations

©Evergreen Public Schools 2010 2

Practice 4: Model with mathematics.

©Evergreen Public Schools 2010 3

Systems of Equations Learning TargetsA-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 $17.27. • How many nickels are in the box?

Suppose you had a box with a total of 519 pennies and nickels worth $17.27. 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 $17.27.

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 $17.27.

How many nickels would you have?

Let’s solve by graphingNumber of coins

x + y = 519

Value of coins5x + y = 17.27

There is something wrong with one of the equations. Fix it!

Suppose you had a box of pennies and dimes with 519 coins worth $17.27.

How many nickels would you have?

Let’s solve by graphingx + y = 519

5x + y = 1727

www.geogebra.org www.desmos.com

Answer the question

x + y = 5195x + 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.