Question 1203239: 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
Found 5 solutions by math_helper, josgarithmetic, math_tutor2020, greenestamps, MathTherapy:
Answer by math_helper(2461)   (Show Source):
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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
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Ans:
Number of quarters = 30
Number of dimes = 33
Check:
25*30 + 10*33 = 750 + 330 = 1080 (ok)
Answer by josgarithmetic(39620)  (Show Source):
Answer by math_tutor2020(3817) (Show Source):
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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):
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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
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):
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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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