(a/k/a: Applying High School Algebra to the Real Word)

I did something like this over at DISBoards several years back, but it’s a good reference so I thought I’d repeat it here, using 2016 prices.

To determine the average cost per credit for the dining plans, it’s best to represent the entitlements as an a equation that sums up to the dollar cost of the plan. There are four components to consider: quick service credits (Q), table service credits (T), snack credits (S), and the rapid fill mug (M, prorated to per-night basis):

```
2Q + S + M = 42.84
T + Q + S + M = 61.84
```

Four unknowns, two equations. Not a good situation. Let’s clean it up a little.

I treat the mug as a souvenir item, and any use you get out of it is a bonus. Plus, it makes the math easier as the retail price of the mug varies based on length of stay. Therefore, the mug value (M) is treated as $0/night.

After that, we’re down to three unknowns but still only two equations. Things get a lot easier if we make one of the unknowns a known. Snack credits (S) have the least potential variability in absolute dollar value, and for the purposes of this exercise, I’m setting it to $4, as most snack items are in the $3-$6 range. The math can be re-run with a different value for S if you think $4 is not an accurate number.

So, let’s re-write our original equations into a form easier to solve:

```
2Q = 42.84 - S - M
T = 61.84 - Q - S - M
```

Subbing in our M and S values:

```
2Q = 42.84 - 4 - 0 = 38.84
T = 61.84 - Q - 4 - 0 = 57.84 - Q
```

We can now solve for Q directly by dividing both sides of the first equation by 2:

```
Q = 19.42
```

And plug that in to solve for T

```
T = 57.84 - 19.42 = 38.42
```

Solving for Deluxe Dining is easier, because we don’t have to differentiate between table service and quick service, just deluxe meal credits (D):

```
3D + 2S + M = 111.73
D = (111.73 - 2S - M) / 3 = (111.73 - 8 - 0) / 3 = 103.73 / 3 = 34.58
```

You can solve for children’s credits (q, t, and d) similarly, and get:

```
q = 6.74
t = 10.22
d = 8.17
```

Ok, now that you have these numbers, how do you use them? Well, they represent the “break even” value of each credit, assuming you’re paying full price for the dining plan of your choice.

So, the first thing to remember about that is that “break even” shouldn’t be treated on a credit-by-credit basis, but as an overall average - it’s okay to go under that value sometimes, as long as you’re going over it often enough to not lose money on the proposition. That said, if paying for the basic dining plan, it’s going to be hard to average much higher than $38 per table service credit, and you may need to “make up for it” by maximizing quick service and snack choices.

Also, remember that when comparing to menu prices, sales tax is already included in the dining plan, so add 6.5% to most menu prices (unless they specifically include tax) for comparison. [I believe some value resorts are in a different tax jurisdiction and charge 7% at their food courts.] For that $38.42 basic TS credit, that’s $36.08 actual menu price and $2.34 sales tax - so you should base your “break even” amount based on the $36.08 menu list price.

Since you’re tipping based on what’s actually ordered, tips should be a wash for comparative items.