Question 231982: A purse contains all of the four types of coins. There are twice as many dimes as nickels. The number of pennies is three less than the number of nickels. There is an equal number of pennies and quarters. The total value of the coins is $3.30. Find the number of each type of coin.
Answer by Robb(9)   (Show Source):
You can put this solution on YOUR website! There are twice as many dimes as nickels.. So
Let x= the number of nickels
And, since there's twice as many dimes as nickels,
Let 2x= the number of dimes
Number of pennies is 3 less than the number of nickels, so
Let x-3= the number of pennies
And since the number of quarters is equal to the number of pennies,
Let x-3 also = the number of quarters.
Now we simply add up all of our variables and numbers and set them equal to the total amount in the purse, $3.30.
But one thing to remember, is since we're working with money, you have to multiply each variable we assigned by the number that represents pennies, nickels, dimes, or quarters... (ie, .01, .05, .10, .25):
This gives us the following equation:
.05x+.10(2x)+.01(x-3)+.25(x-3)=3.30
Notice we multiplied the x variable by the monetary value of each coin..
Now we multiply everything in parenthesis to give us:
.05x+.20x+.01x-.03+.25x-.75=3.30
Now add all the like terms together to give us:
.51x-.78=3.30
(Make sure to keep track of your decimal point while doing this problem, a calculator helps a lot)
The next step is to get x by itself. So let's add .78 to both sides of the equal sign to give us:
.51x=4.08
Then you divide both sides by .51 to get x alone... This gives us:
x=8
Now that we have x=8, we know how many nickels we have. We multiply that number by 2 to find out that we have 16 dimes. Then we subtract 3 from the number of nickels to find out we have 5 pennies, and 5 quarters as well.
You can check this by substituting the numbers we found back into the original equation in place of the variables we assigned:
.05(8)+.10(16)+.01(5)+.25(5)=3.30
.40+1.60+.05+1.25=3.30
Add the left side together and you get:
3.30=3.30, which is true, therefore correct.
Hope this helps!!!
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