Question

Alma is choosing a new smartphone and cellular service plan. Let p be the phone's price in dollars, m be the cost of the selected plan in dollars per month, and C be Alma's total cost in dollars after time t, measured in months of service. Write an equation that expresses C in terms of p, m, and t. Then solve your equation for t.

A) C = p + mt
B) C = pt + m
C) C = p + mt²
D) C = p + mt

Answer 1

Alma's total cost for a smartphone and service plan over time t can be expressed by the equation C = p + mt. To find the time t, the equation can be rearranged to t = (C - p) / m.

Step-by-step explanation:

The question involves creating an equation to express Alma's total cost for a smartphone and cellular service plan after time t, given the phone's price (p) and the monthly plan cost (m). The correct equation to express the total cost C is C = p + mt, which is option D. This linear equation is consistent with the formula provided in chapter 6, and also aligns with common linear equations found in practice tests and self-check questions in relation to budget constraints and linear relationships.

To solve for t when given C, p, and m, we can manipulate the equation as follows: t = (C - p) / m. This gives us the total time in months that Alma will be using the service based on her initial phone purchase price and the monthly plan cost.