Question

Maria rented a coat at $285 for 3 days. If she rents the same coat for 6 days, she has to pay a total rent of $510.

Write an equation in the standard form to represent the total rent (y) that Maria has to pay for renting the coat for x days.

Answer 1

The situation above is an arithmetic sequence with the third term (a3) equal to $285 and sixth term (a6) equal to $510. To determine the nth term of the arithmetic sequence, use the equation,
an = a1 + (n - 1)d
where a1 is the first term and d is the common difference. To solve for these, use the given values,
285 = a1 + (3-1)(d)
510 = a1 + (5 -1)(d)
Solving for the unknowns gives an answer of a1 = 60 and d = 112.5.Thus, the equation is,
y = 60 + 112.5x