18 dimes and 6 quarters
1) Let's recall that 1 dime = $0.10 and a quarter is $0.25
2) We can solve this by writing a Linear System of Equations:
[tex]\begin{gathered} x+y=24 \\ 0.1x+0.25y=3.3 \end{gathered}[/tex]
Note that the second equation relates the quantities in dollars, 330 cents is the same as $3.30.
2.2) So now let's solve it using the Elimination Method multiplying one of those equations by -0.1:
[tex]\begin{gathered} 0.1x+0.25y=3.3 \\ -0.1x-0.1y=-2.4 \\ ---------------- \\ 0.15y=0.9 \end{gathered}[/tex]
Let's divide both sides by 0.15:
[tex]\begin{gathered} \frac{0.15y}{0.15}=\frac{0.9}{0.15} \\ y=6 \end{gathered}[/tex]
So we have 6 coins of quarters, now let's plug into the original equation x+y=24 to get the number of dimes:
[tex]\begin{gathered} x+6=24 \\ x+6-6=24-6 \\ x=18 \end{gathered}[/tex]
3) Hence, there are 18 dimes and 6 quarters
