Steps
So for this, we will create a system of equations. With our information, this is our system (let x = dimes and y = quarters):
[tex]x+y=120\\0.10x+0.25y=25.65[/tex]
So with this system, I will be using the substitution method. With the first equation, subtract y on both sides of the equation:
[tex]x=120-y\\0.10x+0.25y=25.65[/tex]
Now, since we know that x = 120 - y, substitute that into the second equation and solve for y as such:
[tex]0.10(120-y)+0.25y=25.65\\12-0.10y+0.25y=25.65\\12+0.15y=25.65\\0.15y=13.65\\y=91[/tex]
Now that we have the value of y, substitute it into either equation to solve for x:
[tex]x+91=120\\x=29\\\\0.10x+0.25(91)=25.65\\0.10x+22.75=25.65\\0.10x=2.90\\x=29[/tex]
Answer
In short, there are 29 dimes and 91 quarters.
