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?
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?
+237 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
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
