Question 847398
To solve this word problem, we need to first convert the problem into a couple of equations.  Let's see what we know:


We know there are a total of 56 coins, comprised of only dimes and quarters.  In other words


d + q = 56, where d stands for dimes and q stands for quarters.


We also know that the total value of dimes and quarters is $9.50.  We also know that a dime is worth 10 cents and a quarter is worth 25 cents.  In other words


.10d + .25q = 9.50


We now have the two equations we need to solve our problem.  Because there are two equations with 2 unknowns, this is a linear equation, and we will set it up as follows:


   d +    q = 56
.10d + .25q = 9.50


Let's get rid of the decimals from our second equation, to make the equation easier to work with.  To do this, we will multiply our entire second equation by 100, which will give us:


10d + 25q = 950


Now we have


  d +   q = 56
10d + 25q = 950


Next, we need to get rid of one of our variables, so if we multiply our first equation by -10, and then add both equations together, we will be left with only q.  So, when we multiply the first equation by -10, we will have


-10d + -10q = -560
 10d +  25q =  950


When we add both equations together, we will obtain


15q = 390


Dividing both sides of this equation by 15 will give us the number of quarters we have:


{{{15q/15 = 390/15}}} = 


q = 26


Now we know there are 26 quarters.