The owner of a restaurant franchise pays the parent company a monthly fee of
$5163
plus
12
%
of sales.
(a) Write a linear model to compute the monthly payment,
y
, that the restaurant owner must pay the parent company for
x
dollars in sales.
(b) Use the equation from part(a) to compute the amount that the owner has to pay if monthly sales are
$10,700
.
Part: 0 / 2
0 of 2 Parts Complete
(a) Write a linear model to compute the monthly payment,
y
, that the restaurant owner must pay the parent company for
x
dollars in sales.
=y
The linear model to compute the monthly payment, y, that the restaurant owner must pay the parent company for x dollars in sales is:
y = 5163 + 0.12x
(a) The linear model to compute the monthly payment, y, that the restaurant owner must pay the parent company for x dollars in sales can be expressed as:
y = 5163 + 0.12x
(b) To compute the amount that the owner has to pay if monthly sales are $10,700, substitute x = 10,700 into the equation:
y = 5163 + 0.12 * 10,700
= 5163 + 1284
= 6447
Therefore, the owner has to pay $6,447 if the monthly sales are $10,700.
(a) To write a linear model to compute the monthly payment, we can break down the monthly payment into two components: the fixed fee of $5163 and the variable fee of 12% of sales.
The fixed fee stays the same regardless of the sales, so we can represent it as a constant term. The variable fee is calculated as a percentage of the sales, so we can represent it as a proportion of the sales.
Therefore, the linear model to compute the monthly payment, y, that the restaurant owner must pay the parent company for x dollars in sales is:
y = $5163 + 0.12x
(b) To compute the amount that the owner has to pay if monthly sales are $10,700, we simply plug in the value of x into the equation from part (a):
y = $5163 + 0.12x
y = $5163 + 0.12 * $10,700
y = $5163 + $1,284
y = $6,447
So, if the monthly sales are $10,700, the owner has to pay $6,447 to the parent company.