SOLUTION: I'm having trouble understanding how they got the answer this is what the example shows A cashier has 90 dimes and nickels in his cash drawer. If the total value of the coins is

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Question 1060865: I'm having trouble understanding how they got the answer this is what the example shows
A cashier has 90 dimes and nickels in his cash drawer. If the total value of the coins is $6.40,how many nickels are in the drawer?
5x+10(90-x)=640
5x+900-10x=640
-5x=-260
5x=260
X=52
How did they come up with this solution?
Found 2 solutions by josmiceli, MathTherapy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I do this the " long way " which might
be easier to understand
-----------------------
Let +n+ = number of nickels
Let +d+ = number of dimes
--------------------------------
(1) +n+%2B+d+=+90+
(2) +5n+%2B+10d+=+640+ ( in cents )
-----------------------------------
Multiply both sides of (1) by +5+ and
subtract (1) from (2)
(2) +5n+%2B+10d+=+640+
(1) +-5n+-+5d+=+-450+
-------------------------
+5d+=+190+
+d+=+38+
and
(1) +n+%2B+d+=+90+
(1) +n+%2B+38+=+90+
(1) +n+=+52+
There are 52 nickels and 38 dimes
( same as their answer, since +X+ is number of nickels )
---------------------------
check answer:
(2) +5n+%2B+10d+=+640+
(2) +5%2A52+%2B+10%2A38+=+640+
(2) +260+%2B+380+=+640+
(2) +640+=+640+
OK

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

I'm having trouble understanding how they got the answer this is what the example shows
A cashier has 90 dimes and nickels in his cash drawer. If the total value of the coins is $6.40,how many nickels are in the drawer?
5x+10(90-x)=640
5x+900-10x=640
-5x=-260
5x=260
X=52
How did they come up with this solution? 
Let me answer your question

They let the number of nickels be x

Therefore, the number of dimes = 90 - x

With each nickel valued at 5c, or .05, and each dime valued at 10c, or .1, we get the following TOTAL value equation: .05x + .1(90 - x) = 6.4

Now, most people hate working with decimals so to get rid of the decimals, the entire equation is multiplied by 100 to get: 5x + 10(90 - x) = 640

Now, x is solved for and the value for it is 52. Since number of nickels is x, the number of nickels is 52.