Question

assessment practice

1. the cruz family shares a family cell phone plan. the plan is for 3,200 cell phone minutes each month. the father has used 1,200 minutes. the mother has used at least 600 minutes. the two children have used 675 minutes each.

write an inequality that shows the number of minutes the cruz family has used. explain.

Explanation:

Step1: Define variables

Let \( m \) be the number of minutes the mother has used. We know the father used 1200 minutes, each child used 675 minutes (and there are two children), and the total minutes used by the family should be less than or equal to 3200 (since that's the plan's limit).

Step2: Calculate total minutes used

The total minutes used by the family is the sum of the father's minutes, the mother's minutes, and the two children's minutes. The father's minutes: 1200. The mother's minutes: \( m \) (with \( m \geq 600 \)). Each child: 675, so two children: \( 2\times675 = 1350 \). So total minutes used: \( 1200 + m + 1350 \).

Step3: Form the inequality

Since the total minutes used must be less than or equal to the plan's 3200 minutes, the inequality is \( 1200 + m + 1350 \leq 3200 \), which simplifies to \( m + 2550 \leq 3200 \). But we also know \( m \geq 600 \), so combining these (but the main inequality for total usage is based on the plan limit), and since \( m \geq 600 \), we can also write the total usage inequality as \( 1200 + 600 + 1350 \leq 1200 + m + 1350 \leq 3200 \) (but the key inequality for the total is \( 1200 + m + 2\times675 \leq 3200 \), which simplifies to \( m + 2550 \leq 3200 \), and since \( m \geq 600 \), the family's total usage \( T = 1200 + m + 1350 \) satisfies \( 1200 + 600 + 1350 \leq T \leq 3200 \), so \( 3150 \leq T \leq 3200 \) (but the inequality in terms of \( m \) is \( 1200 + m + 1350 \leq 3200 \) with \( m \geq 600 \)).

Answer:

The inequality is \( 1200 + m + 2\times675 \leq 3200 \) (or simplified \( m + 2550 \leq 3200 \) where \( m \geq 600 \)). Explanation: The total minutes used by the family is the sum of the father's 1200 minutes, the mother's \( m \) minutes (with \( m \geq 600 \)), and the two children's minutes (2×675 = 1350). This total must be less than or equal to the plan's 3200 minutes, so we add the minutes and set the sum to be ≤ 3200.