Question

u2l20 practice - writing and solving inequalities in one variable
possible points: 1
diegos goal is to walk more than 70,000 steps this week. the mean number of steps that diego walked during
the first 4 days of this week is 8,019.

1. write an inequality that expresses the mean number of steps that diego needs to walk during the last 3

days of this week to walk more than 70,000 steps. remember to define any variables that you use.

1. if the mean number of steps diego walks during the last 3 days of the week is 12,642, will diego reach his

goal of walking more that 70,000 steps this week?

• 7s > 70,000, where s is the mean number of steps that diego walks during the week.

8019 + 3s > 70,000, where s is the mean number of steps that diego walks during the last 3 days of the
week.
4 · 8019 + 3s > 70,000, where s is the mean number of steps that diego walks during the last 3 days of
the week.

• yes, because 4 · 8019 + 3 - 12,642 = 70,002 which is more than 70,000
• yes, because 7 · 12,642 = 88,494 which is more than 70,000
• no because 8019 + 3 · 12,642 = 45,945 which is less than 70,000.

Explanation:

Step1: Calculate steps in first 4 days

The mean number of steps in first 4 days is \(8019\). So total steps in first 4 days \(=4\times8019\)

Step2: Set up inequality

Let \(S\) be the mean number of steps in last 3 days. Total steps in 7 days \(=4\times8019 + 3S\). Since goal is to walk more than \(70000\) steps, the inequality is \(4\times8019+3S>70000\)

Step3: Check if goal is reached

Substitute \(S = 12642\) into \(4\times8019+3S\).
\(4\times8019+3\times12642=32076+37926=70002\)

Answer:

1. The inequality is \(4\times8019 + 3S>70000\), where \(S\) is the mean number of steps that Diego walks during the last 3 days of the week.
2. Yes, because \(4\times8019+3\times12642 = 70002\) which is more than \(70000\)