Question

thursday 2/12:

1. rachels cell phone company charges $0.10 per minute. she used 350 minutes last month and paid $84. write and solve a linear equation to find her bill next month if she uses 300 minutes.

Explanation:

Step1: Define linear cost model

Let $C$ = total bill, $m$ = minutes used, $b$ = fixed monthly fee. The linear equation is:
$$C = 0.10m + b$$

Step2: Solve for fixed fee $b$

Substitute $C=84$, $m=350$:
$$84 = 0.10(350) + b$$
$$84 = 35 + b$$
$$b = 84 - 35 = 49$$

Step3: Calculate bill for 300 minutes

Use $m=300$, $b=49$ in the equation:
$$C = 0.10(300) + 49$$
$$C = 30 + 49 = 79$$

Answer:

Rachel's bill next month will be $\$79$.