Two girls go on a road trip . They travel x + 5 km on the first day.They travel 2 km more than half of the distance they travel on the first day,...

The distance they drove on the first day: (x+5)
(1)

The distance they drove on the second day: 2 + (x+5)/2
(2)

The distance they drove on the third day: 3 [2 +
(x+5)/2] (3)

The total distance they
travelled:

(1)+(2)+(3) =
5000

We'll substitute
(1),(2),(3).

(x+5) + 2 + (x+5)/2 + 3 [2 + (x+5)/2] =
5000

We'll remove the
brackets:

(x + 5) + 2 + (x+5)/2 + 6 + 3(x+5)/2 =
5000

We'll combine like
terms:

(x + 5) + 8 + 4(x+5)/2 =
5000

(x + 5) + 8 + 2(x + 5) =
5000

3(x+5) = 5000-8

3(x+5) =
4992

We'll divide by 3:

x + 5
= 1664

We'll subtract 5 both
sides:

x = 1664 -
5

x = 1659
km

Verify:

The
distance they drove on the first day:

(x+5)=1659 + 5 =
1664

The distance they drove on the second
day:

2 + (x+5)/2 = 2+1664/2 = 2 + 832 =
834

The distance they drove on the third day: 3 [2 +
(x+5)/2]

3 [2 + (x+5)/2] = 3*834 =
2502

1664 + 834 + 2502 = 5000 Km