Question 50641
<pre><font size = 3 color = "blue"><b>Dana inserted eight coins, consisting of dimes and nickels, into a vending
machine to purchase a Snickers bar for 55 cents. How many coins of each type
did she use?
Book answer: 3 dimes, 5 nickels.

You can do this with one unknown or with two.

With one unknown:P

Let x be the number of dimes.

Then use the principle:  

number in 2nd part = total number - number in 1st part  

                number of nickels = total number of coins - number of dimes

                number of nickels = 8 - x        


Make this chart:

               Worth of each coin   Number of coins       Value          
DIMES                  
NICKELS                 

Now we know that a dime has worth 10¢ and a nickel has worth 5¢

               Worth of each coin   Number of coins       Value          
DIMES                  10 ¢                
NICKELS                 5 ¢            

Next we fill in the number of coins.  We have x dimes and 8-x nickels. So
fill these in:


               Worth of each coin   Number of coins       Value            
DIMES                  10 ¢                x                
NICKELS                 5 ¢              8 - x          


Next we fill in the value of all the dimes by multiplying 10¢ by x dimes,
getting 10x ¢, so fill in 10x ¢ under value of the dimes:


               Worth of each coin   Number of coins       Value          
DIMES                  10 ¢                x                10x ¢
NICKELS                 5 ¢              8 - x         

Next we fill in the value of all the nickels by multiplying 5¢ by 8 - x
nickels, getting 5(8 - x) ¢, so fill that in under value of the nickels:


               Worth of each coin   Number of coins       Value          
DIMES                  10 ¢                x                10x ¢
NICKELS                 5 ¢              8 - x         5(8 - x) ¢ 

Now we can get our equation by the fact that the two expressions under
"value" must total 55¢.

So the equation is  10x + 5(8 - x) = 55

Solve that and get x = 3

So there are 3 dimes

Since there are 8 - x nickels, this is 8 - 3 or 5 nickels.

That's the way using one unknown

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Or, if you want to use two unknowns:

>>...Dana inserted eight coins, consisting of dimes and nickels...<<

Number of dimes + Number of nickels = Number of coins

Translation:                  D + N = 8

>>...into a vending machine to purchase a Snickers bar for 55 cents...<<

Money in the D dimes + Money in the N nickels = Money dropped in machine

                           10D + 5N = 55

So we have the system of 2 equations in one unknown            

                              D + N = 8
                           10D + 5N = 55

Solve that system of equations and get D = 3, N = 5

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Either method is perfectly correct

Edwin</pre></font></b>