Hello There

Ok, so our question states that we have a certain amount of nickels and a certain amount of dimes. these together make $3.95

ok, se we can put this in the form of a simple equation:

if: N = number of nickels

and

if: D = number of dimes

then we know that: N + D = 3.95

this equation is showing us that the number of nickels and the number of dimes is equal to $3.95

no if we look at our second bit of information. it says, that there is now twice the amount of dimes, and that another 21 nickels has been added. This is now equal to $8.40. we know a nickel is equal to 5 cents, or $0.05

So from this we can get another equation:

2D + N + (21 x 0.05) = 8.4

this can be simplified to give:

2D + N + 1.05 = 8.4

Now we can subtract 1.05 from both sides of the equation to give:

2D + N = 7.35

Now we have two equations. these are

N + D = 3.95

2D + N = 7.35

If you look, you can see that the two equations have one thing in common. they both have the same amount of nickels (N). So if they both have the same amount of nickels, then the difference in total is given by the difference in the number of dimes.

So, the first equation has one amount of dimes (D), the second equation has twice that amount of dimes(2D)

so the difference in total will be equal to the difference in dimes.

difference in total: 7.35 - 3.95 = 3.4

the difference in dimes: 2D - D = D

so D = 3.4

this tells us that the number of dimes is equal to $3.40

so we simply divide $3.40 by the amount of one dime ($0.10) to get the number of dimes;

3.4/0.1 = 34

so the number of dimes is equal to 34

if we go back to our original equation: N + D = 3.95

we know the amount of dimes = 34 = $3.40

so we simply replace D with $3.4

this gives us

N + $3.4 = $3.95

now we subtract 3.4 off from both sides to give

N = $0.55

so we know our number of nickels totals $0.55. so as before, we simply divide the nickel total by the amount of one nickel ($0.05)

0.55/0.05 = 11

so the amount of dimes = 34

and the amount of nickels = 11

thank you very much, feel free to post me a question