SOLUTION: how do i solve this problem... 1. Bob has 60 coins consisting of quarters and dimes. The coins combined value is $9.45. Find out how many of each quarters and dimes Bob has. plea

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Question 190626: how do i solve this problem... 1. Bob has 60 coins consisting of quarters and dimes. The coins combined value is
$9.45. Find out how many of each quarters and dimes Bob has. please show me the steps on sloving this...
Found 3 solutions by jim_thompson5910, Alan3354, nerdybill:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"Bob has 60 coins consisting of quarters and dimes" translates to d%2Bq=60. Solve for "q" to get q=60-d. Let's call this equation 1.

Also, "The coins combined value is $9.45" translates to 0.1d%2B0.25q=9.45

Now multiply EVERY term of the last equation by 100 to make every number a whole number to get: 10d%2B25q=945 Let's call this equation 2.

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10d%2B25q=945 Start with the second equation.


10d%2B25%2860-d%29=945 Plug in q=60-d


10d%2B1500-25d=945 Distribute.


-15d%2B1500=945 Combine like terms on the left side.


-15d=945-1500 Subtract 1500 from both sides.


-15d=-555 Combine like terms on the right side.


d=%28-555%29%2F%28-15%29 Divide both sides by -15 to isolate d.


d=37 Reduce.


So there are 37 dimes

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q=60-d Go back to the first equation


q=60-37 Plug in d=37


q=23 Subtract


So there are 23 quarters



Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1. Bob has 60 coins consisting of quarters and dimes. The coins combined value is
$9.45. Find out how many of each quarters and dimes Bob has.
----------------------
Q + D = 60 (60 coins)
25Q + 10D = 945 (total value)
Q = 60 - D (from 1st eqn)
Sub into 2nd eqn
25*(60-D) + 10D = 945
1500 - 25D + 10D = 945
-15D = - 555
D = 37
Q = 23

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Bob has 60 coins consisting of quarters and dimes. The coins combined value is
$9.45. Find out how many of each quarters and dimes Bob has. please show me the steps on sloving this...
.
Let d = number of dimes
then
60-d = number of quarters (since we have a total of 60 coins)
.
.10d + .25(60-d) = 9.45
.10d + 15 - .25d = 9.45
15 - .15d = 9.45
15 - .15d = 9.45
15 = 9.45 + .15d
5.55 = .15d
37 = d (number of dimes)
.
Number of quarters:
60-d = 60-37 = 23 (number of quarters)