Amanda has $5.15 in dimes and quarters. she has eight more quarters than dimes. how many quarters does she have?

Amanda has 17 quarters and 8 dimes.

Step-by-step explanation:

This problem can be solved using a system of equations and the substitution method.  Let 'q' be the number of quarters and 'd' be the number of dimes.  We know that the amount of dimes and quarters is $5.15 or:  0.1d + 0.25q = 5.15.  We also know that there are 8 more quarters than dimes:  q = d + 8.  Substituting the expression 'd+ 8' into the first equation will help us solve for 'd':  0.1d + 0.25(d +8) = 5.15.  Using distributive property and inverse operations, we can solve for d:  0.1d + 0.25d + 2 = 5.15 or 0.35d = 3.15 or d = 9.  Since we now know there are 9 dimes, we can solve for 'q':  q = 9 + 8 = 17.

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50