Family on a road trip. travels x miles on day 1. On day 2 they go 52 miles more than three times the number of miles traveled on day 1. The 3rd day they go 83 miles fewer than day 1. write and simplify an expression for the total number of miles traveled. the answer is 5x-3 but I don't know how they got it. Can you show me?
Day 1. x miles.
2. 3x+52 miles.
3. x-83 miles.
D = x + 3x+52 + x-83 = 5x - 31.
To find the total number of miles traveled over the three days, we need to add up the distances traveled on each day.
Let's break it down step by step:
Day 1: The family travels x miles.
Day 2: They go 52 miles more than three times the number of miles traveled on day 1. Three times the number of miles traveled on day 1 is 3 * x = 3x. So, the distance traveled on day 2 is 3x + 52.
Day 3: They go 83 miles fewer than day 1. So, the distance traveled on day 3 is x - 83.
To calculate the total number of miles traveled, we can add up the distances from each day:
Total distance = Day 1 distance + Day 2 distance + Day 3 distance
= (x) + (3x + 52) + (x - 83)
Now, let's simplify the expression:
Total distance = x + 3x + 52 + x - 83
Combining like terms:
Total distance = 5x + 52 + x - 83
Rearranging terms:
Total distance = 5x + x + 52 - 83
Combining like terms again:
Total distance = 6x - 31
So, the simplified expression for the total number of miles traveled is 6x - 31, not 5x - 3 as you mentioned.