<h3>Answers:</h3><h3>24 dimes</h3><h3>18 nickels</h3>
==============================
Work Shown:
d = number of dimes
n = number of nickels
10d = value of all the dimes in cents
5n = value of all the nickels in cents
10d+5n = total value of all the coins in cents
$3.30 = 3.30*100 = 330 cents
so one equation is 10d+5n = 330
-------
Let's set up the second equation
we have 42 coins, so n+d = 42
subtract d from both sides to get n = 42-d
-------
Go back to the first equation and apply substitution to solve for d.
10d+5n = 330
10d+5(42-d) = 330 ... plug in n = 42-d
10d+5(42)+5(-d) = 330 ... distribute
10d+210-5d = 330
5d+210 = 330
5d = 330-210 ... subtract 210 from both sides
5d = 120
d = 120/5 ... divide both sides by 5
d = 24
-------
Now we can use that to find n.
n = 42-d
n = 42-24 ... plug in d = 24
n = 18
------
Check:
n = 18 nickels
5*n = 5*18 = 90 cents from just the nickels
d = 24 dimes
10*d = 10*24 = 240 cents from just the dimes
5n+10d = 90+240 = 330 cents = $3.30 total from all the coins
n+d = 18+24 = 42 coins total
Answers are confirmed
