Coin Problems Students will use Guess and Check Chart and Algebra to solve Coin Word Problems

What are coins worth? A penny A nickel A dime A quarter .01 .05 .10 .25 What are 5 pennies worth? What are 7 nickels worth? What are 8 dimes worth? What are 9 quarters worth? 5(.01) = .05 7(.05) = .35 8(.10) = .80 9(.25) = 2.25

Setting Up A Guess & Check Chart Set up a column for each coin in problem The last column should be for Total Amount of Money

Bill has four times as many quarters as dimes. He has $2.20 altogether. How many of each coin does he have? D (?) Q (4D) Total (2.20) Key Phrase: Four times as many quarters as dimes This tells us that if we know: how many dimes We can figure out: how many quarters So our guess column will be the Dime column

Bill has four times as many quarters as dimes. He has $2.20 altogether. How many of each coin does he have? The guess column D (?) Q (4D) Total (2.20) 5 20 5(.10) + 20(.25) .50 + 5.00 = 5.50

Bill has four times as many quarters as dimes. He has $2.20 altogether. How many of each coin does he have? D (?) Q (4D) Total (2.20) 5 20 5(.10) + 20(.25) .50 + 5.00 = 5.50 3 12 3(.10) + 12(.25) .30 + 3.00 = 3.30 2 8 2(.10) + 8(.25) .20 + 2.00 = 2.20 Bill has 2 dimes and 8 quarters We found the total!!!

Bill has four times as many quarters as dimes. He has $2.20 altogether. How many of each coin does he have? To convert to Algebraic Equation: The guess column becomes x! D (?) Q (4D) Total (2.20) 2 8 2(.10) + 8(.25) .20 + 2.00 = 2.20 X 4x X(.10) + 4x(.25) = 2.20 The Total Column becomes the equation!

Using Algebra to Solve STEPS Define variables Write an equation Solve equation Answer question !

Bill has four times as many quarters as dimes. He has $2.20 altogether. How many of each coin does he have? The guess column becomes x! D (?) Q (4D) Total (2.20) X 4x x(.10) + 4x(.25) = 2.20 The Total Column becomes the equation! x(.10) + 4x(.25) = 2.20 .10x + 1.00x = 2.20 1.10x = 2.20 x = 2 Answer: Bill has 2 dimes and 8 quarters. Let x = # dimes Let 4x = # quarters Hint: Keep 2 decimal places so your numbers look like money

Paul has twice as many dimes as pennies and 3 times as many nickels as pennies. He has $1.80. How many of each type of coin? Set up chart !!! If we know how many pennies, we can figure nickels & dimes! Start Guessing! P (?) N (3P) D (2P) Total (1.80)

Paul has twice as many dimes as pennies and 3 times as many nickels as pennies. He has $1.80. How many of each type of coin? P (?) N (3P) D (2P) Total (1.80) 2 6 4 2(.01) + 6(.05) +4(.10) .02+.30+.40=.72 4 12 8 4(.01) + 12(.05)+8(.10) .04+.60+.80=1.44 5 15 10 5(.01) + 15(.05) + 10(.10) .05+.75+1.00=1.80 Paul had 5 pennies, 15 nickels, and 10 dimes.

Paul has twice as many dimes as pennies and 3 times as many nickels as pennies. He has $1.80. How many of each type of coin? P (?) N (3P) D (2P) Total (1.80) 5 15 10 5(.01) + 15(.05) + 10(.10) .05+.75+1.00=1.80 X 3x 2x X(.01)+3x(.05)+2x(.10)=1.80 X(.01)+3x(.05)+2x(.10) = 1.80 .01x+.15x+.20x=1.80 .36x=1.80 X=5 Let x = #pennies Let 3x=#nickels Let 2x=#dimes Paul had 5 pennies, 15 nickels and 10 dimes.

Wrapping It Up-Coin Problems How do you label your Guess & Check chart? How do you decide which column is x? What is the most important thing you will do when solving a word problem? All coins and Total Amount The guess column Answer the question!!!!!!