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A jar contains n nickels and d dimes. There are 22 coins in the jar, and the total value of the coins is $1.60. How many nickels and how many dimes are in the jar?

 Mar 15, 2021
 #1
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Let  n  be the number of nickels in the jar  and let  d  be the number of dimes.

 

There are  22  coins in the jar, so we can make this equation:

 

n + d  =  22     Let's subtract  d  from both sides of this equation

 

n  =  22 - d

 

The total value of the coins is  $1.60,  so we can make this equation:

 

0.05n  +  0.10d  =  1.60

                                              We can multiply both sides of the equation through by  10

5n  +  10d   =   160

                                              Since  n = 22 - d  we can substitute  22 - d  in for  n

5(22 - d)  +  10d   =  160

                                              Distribute  5  to each term in parenthesees

110 - 5d  +  10d   =   160

                                              Combine  -5d  and  10d  to get  5d

110 + 5d   =   160

                                              Subtract 110  from both sides of the equation

5d   =   50

                                              Divide both sides of the equation by  5

d   =   10

 

Now that we know  d  =  10   we can find  n  by substituting  1  for  d  in the first equation.

 

n   =   22 - d   =   22 - 10   =   12

 

So there are  12  nickels and  10  dimes.

 Mar 15, 2021
 #2
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n = nickels                              value = 5n

d= dimes = 22-n                     value = 10(22-n)      summed = 160

5n+10(22-n) = 160

-5n = -60

n = 12     the d = 22-n = 10

 Mar 15, 2021

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