Number of quarters: Q

Number of dimes:   63-Q



Expressing everything in terms of cents:



25Q + 10(63-Q) = 1080

15Q + 630 = 1080

15Q = 450  -->  Q = 450/15 = 30  --> number of dimes = 63-30 = 33  



--

Ans:

Number of quarters = 30

Number of dimes = 33



Check:

25*30 + 10*33 = 750 + 330 = 1080 (ok) 

Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
 y number of quarters

63-y number of dimes

$10.8 amount of money





----------simplify and solve.





-----divided both members by 5;

















-------uncomplicated computation





-----quarters 

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!
 

Answer: 30 quarters, 33 dimes







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 = 30 quarters

0 dimes increases to 0+33 = 33 dimes

Those are the final answers.





Check:


Condition 1: Coin Count
Condition 2: Coin Value
30 quarters + 33 dimes = 63 coins total
30 quarters = 30*25 = 750 cents 
33 dimes = 33*10 = 330 cents
750 cents + 330 cents = 1080 cents = $10.80


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.

 

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!
 


I like the semiformal approach used by tutor Math_tutor2020....  But the numbers are easier to work with if you start by considering the case where all 63 coins are dimes.  Then


63 dimes make 63($0.10) = $6.30

The actual total is $10.80, which is $4.50 more than $6.30

The difference between the value of a dime and a quarter is 15 cents, or $0.15

The number of quarters needed to make the additional $4.50 is $4.50/$0.15 = 30


ANSWER: 30 quarters, so 63-30 = 33 dimes


Here is a solution using logical reasoning and one calculator calculation.  This method is not efficient, but it gives you good practice with logical reasoning.


(1) The average value of the coins is $10.80/63 = 17.14 cents approximately.  That average is just a bit closer to 10 cents than to 25 cents, so the number of dimes should be a just a bit more than the number of quarters.

(2) With a total value of $10.80, we know that the number of quarters must be even, and the number of dimes must be 3 more than a multiple of 5.


A bit of logical reasoning with (1) and (2) tells us that almost certainly the answer is 30 quarters and 33 dimes.


And performing a simple calculation verifies that solution to be correct.


30($0.25)+33($0.10) = $7.50+$3.30 = $10.80


 

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
 
stella has 63 coins .the coins are a mixture of quarters and dimes .she has a total of $10.80 . how many quarters and how many dimes does stella have

Let number of quarters she has, be Q
Then number of dimes she has = 63 - Q
We then get: .25Q + .1(63 - Q) = 10.8
              .25Q + 6.3 - .1Q = 10.8
                    .25Q - .1Q = 10.8 - 6.3
                          .15Q = 4.5
     Number of quarters, or   

You should now be able to determine the number of dimes.
 

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