a family travels to Bryce Canyon for three days. on the first day, they drive 150 miles. on the second day, they drive 190 miles. what is the least number of miles they drove on the third day if their average number of miles per day was at least 180?
Well, if they drove 150 miles on the first day and 190 miles on the second day, and their average number of miles per day was at least 180, then on the third day they must have driven... a clown car! Just kidding! Let's calculate it.
To find the least number of miles they drove on the third day, we need to consider the total number of miles they drove and spread it out over the three days.
On the first and second days, they drove a total of 150 + 190 = 340 miles.
To calculate the least number of miles they drove on the third day, we subtract the total miles driven on the first two days from the minimum average number of miles per day times 3.
So, (180 * 3) - 340 = 540 - 340 = 200 miles.
Therefore, the least number of miles they drove on the third day is 200 miles.
To find the least number of miles they drove on the third day, we can use the average number of miles per day as a guideline.
Let's denote the number of miles they drove on the third day as "x".
The total number of miles driven over three days is the sum of the distances driven each day: 150 miles + 190 miles + x miles.
To find the average number of miles per day, we divide the total number of miles driven by three: (150 + 190 + x) / 3.
We want this average to be at least 180, so we can write the following inequality:
(150 + 190 + x) / 3 ≥ 180
To solve for x, we can multiply both sides of the inequality by 3:
150 + 190 + x ≥ 540
Now, let's simplify the inequality:
340 + x ≥ 540
Subtract 340 from both sides:
x ≥ 200
Therefore, the least number of miles they drove on the third day is 200 miles.
To find the least number of miles the family drove on the third day, we need to determine the minimum distance required for them to maintain an average of at least 180 miles per day.
Let's break it down step by step:
1. Add the distances traveled on the first two days: 150 miles + 190 miles = 340 miles.
2. Determine the minimum distance required on the third day to achieve an average of 180 miles per day:
- Let's assume the minimum distance on the third day is x miles.
- We know that the total distance covered should be at least 3 times the average distance per day. So, the total distance equals 3 * 180 miles = 540 miles.
3. Set up an equation to solve for x:
- Total distance = Distance on the first day + Distance on the second day + Distance on the third day
- 540 miles = 340 miles + x miles
4. Solve for x:
- Subtract 340 miles from both sides of the equation:
x miles = 540 miles - 340 miles
x miles = 200 miles
Therefore, the least number of miles the family must drive on the third day to maintain an average of at least 180 miles per day is 200 miles.
Mean = Σx/n
180 = (150+190+x)/3
Solve for x.