Question 1203239
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Answer: <font color=red size=4>30 quarters, 33 dimes</font>



Explanation


Consider the scenario that Stella has 63 quarters and 0 dimes.


63 quarters = 63*25 = 1575 cents = 1575/100 = $15.75


This is not the $10.80 that we want, so we'll need to swap a few quarters for some dimes.


x = number of times we replace one quarter with one dime


Each time we do this replacement, the net value goes down by 15 cents because 25-10 = 15 is the gap value between a quarter and a dime. The expression 15x represents the total decrease amount.


We need the value to go from $15.75 to $10.80
This is a gap of $15.75 - $10.80 = $4.95 = 495 cents
Therefore, we need the value to decrease by 495 cents.


15x = total decrease
15x = 495
x = 495/15
x = 33
We must replace 33 quarters with dimes.


63 quarters drops to 63-33 = <font color=red>30 quarters</font>
0 dimes increases to 0+33 = <font color=red>33 dimes</font>
Those are the final answers.


Check:
<table border = "1" cellpadding = "5"><tr><td>Condition 1: Coin Count</td><td>Condition 2: Coin Value</td></tr><tr><td>30 quarters + 33 dimes = 63 coins total</td><td>30 quarters = 30*25 = 750 cents <br>33 dimes = 33*10 = 330 cents<br>750 cents + 330 cents = 1080 cents = $10.80</td></tr></table>
Both conditions have been met to fully confirm the answers.


To get everything on one line for condition 2, we could write: 
30 quarters + 33 dimes = 30*25+33*10 = 1080 cents = $10.80
However, it might be better to split it into multiple lines to make it more readable.
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