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Math

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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

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