Step 6 – Now that we know x we can find all the solutions. Go back to your unknowns and algebraic expressions. If you plug in 17 for x in all of them you will have your answers. # of liberals = 2x = 2(17) = 34 # of moderates = x = 17 # of conservatives = x+7 = 17+7 = 24 Step 7 – So our answer is 34 liberals, 17 moderates and 24 conservatives. Does this answer make sense? Yes. There are twice as many liberals and seven more conservatives than moderates and the total is 75. Let’s look at another example. Jimmy has a bunch of coins in the cushions of his couch. As he is out of money and needs gas in his car, he is searching for as many coins as he can find. The coins he found had a total value of $7.50 . He only found quarters, dimes and nickels. There were three times as many dimes as nickels and eighteen more quarters than nickels. How many of each type of coin did he find? Step 1 – Write down all unknowns. You should write down the following on a piece of paper. Again the key thing to remember is that for coin problems, the number of coins is not money. If we have 3 quarters, that does not mean I have $3. You need to multiply the number of the coins times the value of the coin. So 3 quarters means 3 x 0.25 = $0.75 . Not only do we need to know how many coins but also we need algebraic expressions that represent the amount of money for each coin. # of nickels = # of dimes = # of quarters = $ in nickels = $ in dimes = $ in quarters = Step 2 – Since we know something about quarters and dimes but nothing about nickels we will let x be the number of nickels. Step 3 – Three times as many dimes as nickels means we can represent the number of dimes as 3x. Eighteen more quarters than nickels means we can represent quarters with x + 18. Remember to get the amount of money, we will multiply the number of nickels times its value ($0.05), the number of dimes times its value ($0.10) and the number of quarters times its value ($0.25). We can simplify each expression. For the quarters we will use the distributive property.
Step 6 – Now that we know x we can find all the solutions. Go back to your unknowns and algebraic expressions. If you plug in 17 for x in all of them you will have your answers. # of liberals = 2x = 2(17) = 34 # of moderates = x = 17 # of conservatives = x+7 = 17+7 = 24 Step 7 – So our answer is 34 liberals, 17 moderates and 24 conservatives. Does this answer make sense? Yes. There are twice as many liberals and seven more conservatives than moderates and the total is 75. Let’s look at another example. Jimmy has a bunch of coins in the cushions of his couch. As he is out of money and needs gas in his car, he is searching for as many coins as he can find. The coins he found had a total value of $7.50 . He only found quarters, dimes and nickels. There were three times as many dimes as nickels and eighteen more quarters than nickels. How many of each type of coin did he find? Step 1 – Write down all unknowns. You should write down the following on a piece of paper. Again the key thing to remember is that for coin problems, the number of coins is not money. If we have 3 quarters, that does not mean I have $3. You need to multiply the number of the coins times the value of the coin. So 3 quarters means 3 x 0.25 = $0.75 . Not only do we need to know how many coins but also we need algebraic expressions that represent the amount of money for each coin. # of nickels = # of dimes = # of quarters = $ in nickels = $ in dimes = $ in quarters = Step 2 – Since we know something about quarters and dimes but nothing about nickels we will let x be the number of nickels. Step 3 – Three times as many dimes as nickels means we can represent the number of dimes as 3x. Eighteen more quarters than nickels means we can represent quarters with x + 18. Remember to get the amount of money, we will multiply the number of nickels times its value ($0.05), the number of dimes times its value ($0.10) and the number of quarters times its value ($0.25). We can simplify each expression. For the quarters we will use the distributive property.