Question

9 multiple choice 1 point nora works at a donut shop. at the end of her shift, the change in the tip jar totals $13.05. the jar contains quarters, dimes, and nickels. the number of dimes is 3 more than twice the number of nickels and the number of quarters is 1 less than three times the number of nickels. find the number of dimes in the jar. 16 29 38 13 clear my selection

Explanation:

Step1: Define variables

Let the number of nickels be $n$. Then the number of dimes $d = 2n + 3$, and the number of quarters $q = 3n - 1$.

Step2: Set up the value equation

The value of nickels is $0.05n$, dimes is $0.10d$, and quarters is $0.25q$. The total value is $13.05$, so:
$$0.05n + 0.10d + 0.25q = 13.05$$

Step3: Substitute $d$ and $q$ in terms of $n$

Substitute $d = 2n + 3$ and $q = 3n - 1$ into the equation:
$$0.05n + 0.10(2n + 3) + 0.25(3n - 1) = 13.05$$

Step4: Expand and simplify

Expand the terms:
$$0.05n + 0.20n + 0.30 + 0.75n - 0.25 = 13.05$$
Combine like terms:
$$(0.05n + 0.20n + 0.75n) + (0.30 - 0.25) = 13.05$$
$$1.00n + 0.05 = 13.05$$

Step5: Solve for $n$

Subtract $0.05$ from both sides:
$$n = 13.05 - 0.05 = 13$$

Step6: Find the number of dimes

Now, substitute $n = 13$ into $d = 2n + 3$:
$$d = 2(13) + 3 = 26 + 3 = 29$$

Answer:

29 (corresponding to the option "29")