SOLUTION: A person has a bag containing quarters and dimes. There are a total of 66 coins in the bag, and the total value of the coins is $10.95.
Determine how many quarters and dimes are
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-> SOLUTION: A person has a bag containing quarters and dimes. There are a total of 66 coins in the bag, and the total value of the coins is $10.95.
Determine how many quarters and dimes are
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Question 1202529: A person has a bag containing quarters and dimes. There are a total of 66 coins in the bag, and the total value of the coins is $10.95.
Determine how many quarters and dimes are in the bag.
There are quarters.
There are dimes. Found 2 solutions by math_tutor2020, josgarithmetic:Answer by math_tutor2020(3816) (Show Source):
Consider hypothetically the bag has all 66 coins as quarters.
(66 quarters)*(25 cents a piece) = 1650 cents = $16.50
This value is too large because we want $10.95 instead (aka 1095 cents)
Subtract the values to find the gap
$16.50 - $10.95 = $5.55 = 555 cents
We need to lower the value by 555 cents.
To do this, we replace some quarters with dimes.
Replace 1 quarter with 1 dime to reduce the amount by 15 cents (since 25 - 10 = 15)
Do this type of replacement n times and we've reduced it by 15n cents.
15n = 555
n = 555/15
n = 37
We'll need to do the replacement of "1 quarter --> 1 dime" 37 times.
66 quarters drops down to 66-37 = 29 quarters
0 dimes bumps up to 0+37 = 37 dimes
The check section is provided at the bottom.
As a slight alternative, try to start with 66 dimes and do the replacement "1 dime --> 1 quarter".
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Method 2
q = number of quarters
66-q = number of dimes
Those two expressions add to 66 coins total.
25q = cents value of the quarters only
10(66-q) = 660-10q = cents value of the dimes only
25q+(660-10q) = 15q+660 = total value in cents
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