Answer:
a) 4(8019) +3s ≥ 70000
b) yes
Explanation:
Diego has walked an average of 8019 steps per day for 4 days and wants to walk 70000 steps in a week. You want an inequality for the average number of steps per day that Diego must walk for the last 3 days of the week, and you want to know if 12642 is a solution.
a) Inequality
The inequality will express the relationship between the steps walked and the goal. Let s represent the average number of steps walked each day for the last 3 days of the week.
The total number of steps walked in the first 4 days is the average per day times the number of days: 4(8019). The total number of steps walked in the last 3 days is the average per day times the number of days: 3s.
The total for the week is the sum of these. We want that to exceed 70000:
4(8019) +3s ≥ 70000 . . . . . . . the desired inequality
b) Solution
Solving for s, we find ...
3s ≥ 7000 -4(8019)
3s ≥ 37924 . . . . . . . . . subtract 32076
s ≥ 12641 1/3 . . . . . . . . divide by 3
The offered number, 12642, is greater than 12641 1/3, so is a solution.
Diego will meet his goal if he averages 12642 steps per day for the last 3 days of the week.
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Additional comment
If Diego's 3-day average is 12462, he will have walked 70002 steps for the week, a number that is more than 70000.