This problem seems to be a case of system of equations. We can represent the given parameters using variables and solve by substitution or elimination.
d-will represent dimes and q will represent quarters.
the total amount of dimes and quarters combined is 59, so d+q=59
in addition d=.10 (a dime is worth 10 cents) and q=.25 (a quarter is worth .25 cents).
.10d represents the total value of the dimes in the jar combined, and .25q represents the total value of the quarters in the jar combined.
The total value of both dimes and quarters in the jar is equal to $9.65, thus:
.10d+.25q=9.65
So now we have:
d+q=59
.10d+.25q=9.65
I will solve by elimination. The goal of elimination is to eliminate one of the variables. So you will choose variable to eliminate (in this case I will choose d). Then you will multiply both equations by the necessary constant to have it so that one equation has a coefficient of some value (for the variable you want to eliminate), and the other equation has a negative coefficient of the same value (for that same variable).
(-.10)(d+q)=59(.10)
.10d+.25q=9.65
-.10d-.10q=-5.9
.10d+.25q=9.65
___________________
.15q=3.75
.15q/.15=3.75/.15
q=25
We will now plug this value into one of the equations to get the value of the other variable (the problem doesn't require the second value, but it is good to have practice solving for both variables and checking your work)
d+q=59
d+25=59
d+25-25=59-25
d=34
You can plug both of these values into the second equation to check your work
