Start with the easy sentence first:
"She has a total of 21 coins."
Let d = the number of dime coins and n = the number of nickel coins.
Then if you add them together you put a + sign between them like this
d+n
and since the total number of coins is 21, we have the equation
d+n = 21
Now look at the other clause:
"...$1.65 in dimes and nickels."
If you multiply the number of dimes, d, by 10 cents you get 10d cents
If you multiply the number of nickels, n, by 5 cents you get 5n cents
If you add 10d cents and 6n cents, you put a + sign between them, like
this:
10d+5n
That expression must represent the total number of cents.
But you also know that the total number of cents in $1.65 is 165 cents.
So 10d+5n must equal to 165. So you have the equation
10d+5n = 165
So you have the systme of equations
d+n = 21
10d+5n = 165
which you can solve by substitution or elimination and get d=12, n=9
If you don't know how to solve that system of equations, then
post again asking how.
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Suppose Tom has 14 coins totaling $2.30. If he has only dimes and quarters,
how many of each does he have?
The exact same way. You'll get d=8, q=6
Edwin