Please Help on this word problem.?

Question

A swimmer plans to swim at least 100 laps during a 6 day period. During this period, the swimmer will increase the number of laps completed each day by one lap. What is the least number of laps the swimmer must complete on the first day ?

Answer 1

15

Day 1: x
Day 2: x+1
Day 3: x+2
Day 4: x+3
Day 5: x+4
Day 6: x+5

6x + 15 >= 100
6x >= 85
x >= 85/6 = 14.25

For whole laps, x>= 14.25, the next whole number up is 15

Answer 2

Let x denote the fewest numbr of laps that the swimmer must swim on the first day. This implies the swimmer must swim at least x+1 laps the second day, x+2 laps the third day, and so on, through x+5 laps on the sixt day. So the problem is to find the value x that satisfies:

x+x+1+x+2+x+3+x+4+x+5>=100
6x+15>=100
x>=(100-15)/6

Presumably, the answer is an integer, since partial laps may no count. If so, then x=15 is the fewest laps that the swimmer must swim the first day.

Answer 3

if x the number of laps in the first day then x+1 is for the second and x+2 for the third .....
so x+x+1+x+2+x+3+x+4+x+5=100
then 6x=85
x=85/6=14.1666
so the least number of laps on the first day is 15.

Answer 4

x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)=100
or 6x+15=100
6x=85
x=14.16 so, to reach a 100 on the sixth day, the swimmer must start out with a minimum of 15 laps.

Answer 5

Answer: 15 laps

x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)=100

6x+15=100
6x=85
x=85/6

x=15 laps

Answer 6

It's an arithmetic series with
a + (a+1) + (a+2) + (a+3) + (a+4) + (a+5) = 100
6a + 15 = 100
a = 14.17

The minimum is 15

Answer 7

13 :-)