I can help you to find the answer changing a little bit the question....
You simply need to substitute the values to find the right answer
You can set up a simple equation.
0.25x+0.10y=34.60
x+y=238
You can solve this by any method you like, if I do elimination Multiplying the first one by 4, I can isolate y from the second one substracting 4 times the first one from the second one.
x+y=238
-(x+0.4y=138.4)
= 0.6y=99.6
Y=99.6/0.6= 166.
That means there are 166 dimes or$16.6 in dimes.
Now we can substitute in the first equation and x+166=238.
So there are 72 quarters in the jar