Question

A jar of coins has only dimes and quarters in it. Combined there are a total of 120 coins. The total of all the coins is $25.65. How many dimes and quarters are there?

Answer 1

Steps

So for this, we will create a system of equations. With our information, this is our system (let x = dimes and y = quarters):

`x+y=120\\0.10x+0.25y=25.65`

So with this system, I will be using the substitution method. With the first equation, subtract y on both sides of the equation:

`x=120-y\\0.10x+0.25y=25.65`

Now, since we know that x = 120 - y, substitute that into the second equation and solve for y as such:

`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`

Now that we have the value of y, substitute it into either equation to solve for x:

`x+91=120\\x=29\\\\0.10x+0.25(91)=25.65\\0.10x+22.75=25.65\\0.10x=2.90\\x=29`

Answer

In short, there are 29 dimes and 91 quarters.