I think the answer might be 21?
Substituting this into the other ODE gives
Since , it follows that . The ODE in has characteristic equation
with roots , admitting the characteristic solution
From the initial conditions we get
So we have
Take the derivative and multiply it by -1/4 to get the solution for :
Well one third is 100
so two thirds must be 200
The answer is 10 quarters because 10 quarters would be $2.50. You would need 3 more nickles to get $2.65. 10 would be 7 more than 3.