Question

You are buying cupcakes for a school party. They are in a package of 6 for $8.50. You have budgeted no more than $40 to spend. If cost of the cupcakes is a function of the number of packages purchased, what is the largest element of the domain in this situation?

Answer 1

Answer: Largest element in the domain is 4

The largest number of packages you can buy is 4

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Step-by-step explanation:

1 package costs 8.50*1 = 8.50 dollars

2 packages cost 8.50*2 = 17 dollars

3 packages cost 8.50*3 = 25.50 dollars

and so on. In general

x packages cost 8.50*x = 8.50x dollars

where x is a place holder for a positive whole number (1,2,3,...)

The total amount spent is 8.50x and the budget is $40

This means,

`8.50x \le 40\\\\x \le (40)/(8.50)\\\\x \le 4.70588\\\\x \le 4\\\\`

We round down regardless of how close we are to 5.

If x = 4, then 8.50*x = 8.50*4 = 34

While if x = 5, then 8.50*x = 8.50*5 = 42.5

So we see we go over budget if we buy x = 5 packages.

This makes x = 4 the largest in the domain.

Recall the domain is the set of allowed x inputs. In this case, x is a positive whole number (since we can't buy half a package for instance).