A bank contains 30 coins, consisting of nickels, dimes, and quarters. There are twice as many nickels as quarters and the remaining coins are dimes. If the total value of the coins is $3.35, what is the number of each type of coin in the bank?

Question

lgbasallote · Answer

let n = nickel
d = dime
q = quarters

twice as many nickels as quarters...
2n = q
remaining is dimes...
30 - (2n +n) = d

5(cents) n  + 10(cents) dimes + 25 (cents) quarters = 335 cents

n + q + d = 30
2n - q = 0
5n + 10d + 25q = 335

we now do systems....

-10n - 10d - 10q = -300
5n +  10d + 25q = 335
-5n + 15q = 35

another system...

-5n + 15q = 35
2n - q = 0

-5n + 15q = 35
30n - 15q = 0
25n = 35
n = 7/5

is this right??? ill just continue...

2(7/5) = q
14/5 = q

n+ q + d = 30

d = 30 - n -q
d = 30 - 7/5 - 14/5
d = 150/5 - 21/5
d = 129/5

let's check...

5(7/5) + 10(129/5) + 25(14/5) = 335?
7 + 258 +70 = 335?
335 = 335

i just dont get why the n, d and q arent whole...

lgbasallote · Answer

hmmm it seems when it's n = 2q...we'll have whole numbers..was my representation wrong??

anonymous · Answer

Let n, d and q be the number of nickels, dimes and quarters respectively.
Solve the following three euqations for n, d and q.$$\left\{d+n+q=30,\frac{n}{q}=2,10 d+5 n+25 q=335\right\} $$$$\{n=14,d=9,q=7\} $$

anonymous · Answer

Sorry, the word equations was misspelled.