SOLUTION: there are pennies, nickels , dimes , and quarters in a piggy bank. if there are 14 coins in the bank and their value is $1.05

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Question 1033082: there are pennies, nickels , dimes , and quarters in a piggy bank. if there are 14 coins in the bank and their value is $1.05


Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52809)   (Show Source): You can put this solution on YOUR website!
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there are pennies, nickels , dimes , and quarters in a piggy bank. if there are 14 coins in the bank and their value is $1.05
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Although the condition is discontinued by an obvious way, I can suggest that 

1) all necessary data is presented,  and
2) the question is "how many coins of each value are there in the bank?"


Answer. 2 quarters, 3 dimes, 4 nickels and 5 pennies.

Check.  2*25 + 3*10 + 4*5 + 5*1 = 105,
        2    + 3    + 4   + 5    = 14.


Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Four unknown variables and two equations. The easiest restriction is on how many quarters, being some natural number from 1 to 4.

p, n, d, q the count of each coin.

from account of the money value

the account of the coins


Solve each for p and equate.






CASES FOR THE QUARTERS
q=4


-
q=3


-
q=2

-
q=1

-
Which of these cases will work to give the right whole number values for n and d?


Look at a graph for case q=1. Treat vertical axis as d, horizontal as n,
looks bad!


The graph n and d for case q=2,
guess is that still not good.


See for case q=3,

Maybe....

A different way could be play with the simplest combination of coins to give $1.05 and split some coins to get a count of 14.
, c for count of coins but we must have c=14. Splitting the nickel might not help much, at least not yet.

Split one quarter.
----still not enough coins c.

Split one more quarter.
----we want to be able to get an even number of coins.

Maybe split one nickel from that.
-----we want ONE more coin, so maybe split one dime.

-----THIS must be the combination.
2 quarters
3 dimes
4 nickels
5 pennies
--That is 14 coins.
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