Two girls go on a road trip They travel x 5 km on the firs

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, on the second day. On the third day they drove three times as far as they did on the second day. If they drove 5000 km find the value of x.

Solution

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