Question 1203239
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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<br>
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<br>
ANSWER: 30 quarters, so 63-30 = 33 dimes<br>
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.<br>
(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.<br>
A bit of logical reasoning with (1) and (2) tells us that almost certainly the answer is 30 quarters and 33 dimes.<br>
And performing a simple calculation verifies that solution to be correct.<br>
30($0.25)+33($0.10) = $7.50+$3.30 = $10.80<br>