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Amanda has a total of two hundred four coins. She has three times as many dimes as nickels and one-half as many nickels and one-half as many nickels as pennies. How much money does she have?

 Jan 11, 2022
 #1
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d = 3n

n = 1/2 p    or   p = 2n

p

 

d + n + p = 204       all of this is givenin the question

3n  + 1/2 p    + p  = 204      make some substitiutions form the above equations

3 (1/2 p)    + 1/2 p   + p = 204       now you can compute p = 68        <===== can you finish?

 Jan 11, 2022
 #2
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Let the number of pennies that Amanda has be 'p'.

It is given that she has one-half as many nickels as pennies

So, number of nickels = 1/2

It is given that she has three times as many dimes as pennies

So, number of dimes = 3 * 1/2 = 3p/2

Now, she has a total of 204 coins. So,

           p + p/2 + 3p/2 = 204

      => (2p + p + 3p)/2 = 204

      => 6p = 2 * 204

      => p = 408/6 = 68

So, Amanda has 68 pennies

So, number of nickels = p/2 = 68/2 = 34

and number of dimes = 3p/2 = (3 * 68)/2 = 102

Now, 1 penny = $0.01

         1 nickels = $0.05

    and 1 dimes = $0.10

So, the total money that Amanda has

    = $0.01 * 68 + $0.05 * 34 + $0.10 * 102

    = $0.68 + $17 + $10.2

    = $12.58

 Answer: $12.58 

 Jan 14, 2022
 #3
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Given Amanda has total 204 coins 

she has 3 times as many dimes as nickels 

              1/2 times as many nickels as pennies 

               we can write

                 d = 3n ---- (1)

                 n = 1/2 * p      ;   n = no. of nickels

                 p = 2n ---- (2)     d =  "   " dimes 

                                           p =  "   " pennies 

             Total no. of coins = 204

          => no. of nickels + no. of dimes + no. of pennies = 204

          => n + d + p = 204

          => n + 3n + 2n = 204 => 6n = 204 => n = 34

       => p = 68 and d = 102

She has total 34 * 5 + 102 * 10 + 68 * 1 = 1258 cents

 Jan 16, 2022

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