SOLUTION: Write and expression for the term: The amount of money in cents in a jar containing d dimes and some nickels and quarters, if there are 3 times as many nickels as dimes and twice

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Question 122032: Write and expression for the term:
The amount of money in cents in a jar containing d dimes and some nickels and quarters, if there are 3 times as many nickels as dimes and twice as many quarters as nickels.
I tried to work it out with t being total amount in jar and d=dimes, n=nickels, q=quarters and stating d=3n and n=2q but I cannot put this in an expression that makes sense!
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
The amount of money in cents for each nickel is 5n, for each dime 10d, and for each quarter 25q.

Your equations for the relationship between the numbers of dimes and nickels and between the numbers of quarters and nickels are backwards.

"3 times as many nickels as dimes" means for every dime there are 3 nickels, or n=3d. Likewise, twice as many quarters as nickels would be q+=+2n.

The basic expression for total amount, t, in the jar would be:
t=5n%2B10d%2B25q. But given the other information, you can express the total amount in terms of the number of any one of the coins:

In terms of nickels:
n=3d, so d=n%2F3
q=2n
Substituting:
t=5n%2B10%28n%2F3%29%2B25%282n%29=5n%2B10n%2F3%2B50n=15n%2F3%2B10n%2F3%2B150n%2F3=175n%2F3.

In terms of dimes:
n=3d
q=2n=2%283d%29=6d

Substituting:
t=5%283d%29%2B10d%2B25%286d%29=15d%2B10d%2B150d=175d

In terms of quarters:
q=2n so n=q%2F2
d=n%2F3 so d=%28q%2F2%29%2F3=q%2F6

Substituting: