We have 20 coins in total, lets say that we have X amount od quarters(0.25 dollar) and Y amount of dimes(0.1 dollar), and in total we have $3.05, with this we can write the system:
[tex]X+Y=20[/tex]Wich means that we have 20 coins, and:
[tex]0.25X\text{ + 0.1Y=3.05}[/tex]Thats the amount of money we have.
So, from the first equation, we can isolate X, as follows:
[tex]X=20-Y[/tex]And with that we can substitute X in the second equation, as follows:
[tex]0.25X\text{ + 0.1Y=3.05 }\rightarrow\text{ }0.25(20-Y)\text{ + 0.1Y=3.05 }\rightarrow\text{ }5-0.25Y+0.1Y=3.05[/tex][tex]5-0.25Y+0.1Y=3.05\rightarrow-0.15Y=-1.95\rightarrow Y=13[/tex]So, if Y=13, we have that X=7. So 13 dimes and 7 quarters.
