Acollection of dimes and quarters is worth $6.50. there are 35 coins in all. how many dimes are there?

write the correct systems of equation and solve

Lets do this like this:
X = number of quarters and y=number of dimes.
Now, we know that the total number is 35 and that the change adds up to 6.50.
One equation we can form is x+y=35Remember the total number of coins is 35.
The other equation is 25x+.1y=6.5Because the number of dimes times their value plus the number of quarters times their value gives us a total of 6.5. Now we can solve for x or y easily in the first equation.
Solving for y like this:y=35−xWe can substitute this into the other equation to obtain.25x+.1(35−x)=6.5This simplifies to.15x+3.5=6.5.15x=3x=20
I hope this can help you indeed