Question

The expression 1.04 (0.9x) + 50 represents the total cost of a catered meal at a conference.The organizers of the conference were given a reduction in the cost of the catered meal due to the size of the event. Sales tax wascharged on the reduction price The organizers were also charged a set-up fee. The variable x represents the price of catered mealbefore the reduction.

Answer 1

Answer:

- The set-up fee is $50 ---- True

- The organizers were given a 10% discount on the catered meal. ---- True

Explanation:

Given that the expression that represent the total cost of a catered meal at a conference is;

$1.04(0.9x)+50$

The organizers of the conference were given a reduction in the cost of the catered meal due to the size of the event.

let a represent the percentage discount;

$(1-\frac{a}{100})x$

Sales tax was charged on the reduction price;

let b represent the sales tax;

$(1+\frac{b}{100})(1-\frac{a}{100})x$

The organizers were also charged a set-up fee.

Let c represent the set-up fee;

$(1+\frac{b}{100})(1-\frac{a}{100})x+c$

Comparing to the given equation;

$\begin{gathered} c=\text{ \ 50} \\ (1-\frac{a}{100})=0.9 \\ a=10\text{\%} \\ (1+\frac{b}{100})=1.04 \\ b=4\text{\%} \end{gathered}$

So,

discount = 10%

sales tax = 4%

set up fee = $50.

Now let us determine which of the given options are true;

- The cost of the catered meal was less than the set-up fee -- Not enough information, Probably false.

- The sales tax rate was 10% -- false ( sales tax rate is 4%)

- The set-up fee is $50 ---- True

- The organizers were given a 10% discount on the catered meal. ---- True