SOLUTION: Your piggy bank has a total of 46 coins in it; some are dimes and some are quarters. If you have a total of $7.00, how many quarters and how many dimes do you have? Can you show al

Algebra ->  Systems-of-equations -> SOLUTION: Your piggy bank has a total of 46 coins in it; some are dimes and some are quarters. If you have a total of $7.00, how many quarters and how many dimes do you have? Can you show al      Log On


   

Question 326894: Your piggy bank has a total of 46 coins in it; some are dimes and some are quarters. If you have a total of $7.00, how many quarters and how many dimes do you have? Can you show all of your work so I can understand it better? Thanks in advance!
Found 2 solutions by Fombitz, solver91311:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let D be the number of dimes, Q quarters.
Total number of coins:
1.D%2BQ=46
Total value of coins:
10D%2B25Q=700
2.2D%2B5Q=140
From eq. 1,
D=46-Q
Substitute in eq. 2,
2%2846-Q%29%2B5Q=140
92-2Q%2B5Q=140
3Q=48
highlight%28Q=16%29
Then,
D=46-Q
highlight%28D=30%29

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let represent the number of dimes.

Let represent the number of quarters.

Since dimes are worth 10 cents, the value of all of the dimes in cents is

Likewise the value of all of the quarters is

Since I expressed the value of the coins in terms of cents, let's express the total value of the coins in cents as well. cents.

We know there are 46 coins, so:



And we know the total value of the coins is 700 cents, so:



Rearrange the first equation:



Substitute:



Now all you need to do is solve for and follows directly.

John