Town B is between A&C, the distance frm A to C is 41 miles. BC is 2miles more than twice AB?

Question

(Towns A, B, C, and X are located along a straight highway)

question 1: write an equation and solve it to find AB and BC

question 2: town X is between A and B, 6 miles from A. Find XC?

Answer 1

Let the distance between towns A and B be x miles

So distance between distance B and C is 2x + 2 miles.

So total = 41

So 2x + 2 + x = 41 => x = 13 miles = AB, BC = 28

Answer 2

1.   From the given: 1.   AC = AB + BC  

                             2.   BC = 2 + 2AB (translate the 2nd sentence to algebra)

            and            3.  AC = 41

You can substitute in AC and BC from equations 2 and 3 into the first equation.

AC = AB + BC

41 = AB + (2+2AB)

This simplifies to 41 = 3AB + 2

39 = 3 AB (subtract 2 from each side)

13 = AB (divide both sides by 3)

So AB is 13, and now you can find BC using the very first equation up there:  BC=2+2AB    =  2+2(13)  = 29.

2)  AX+XC = 41

   AX=6

so

     6+XC=41  

  or XC = 35 (subtract 6 from both sides)

Answer 3

for the time being lets make AB = x so the queation looks simpler.

now it states that is (2) miles more than twice ab so then Bc will be

2x + the 2 miles all adding up to 41 metres

so now we can have the equation

x+2x+2 = 41

= 3x +2 = 41

carry 2 to the othside wich gives3x= 39

so x = 13 so the distance of AB is 13

and Bc is twice the lenght plus 2 miles

so 2*13 + 2

makes bc = 28

town X is just 41-6 which then leaves XC = 35 miles

Answer 4

Given:

AC = 41

BC = 2(AB) + 2 Eqn1

Equation:

AB + BC = AC Eqn2

Substitute the given data into Eqn2, then solve for AB:

AB + [2(AB) + 2] = 41

AB + 2(AB) + 2 = 41

3(AB) = 39

AB = 13 miles

Substitute to Eqn2, the solve for BC:

BC = 2(AB) + 2

BC = 2(13) + 2

BC = 28 miles

AX = 6

AC = 41

Equation:

AX + XC = AC

6 + XC = 41

XC = 41 - 6

XC = 35 miles

Answer 5

let us consider that the distance between AB is P:

thererfore, P + 2P + 2 = 41

                P = 39/3 = 13

therefore, AB= 13 & BC = 28

thus, XC = 41- 6 = 35

Answer 6

A---------------X--------------B--------...

            a                                 2a+2  

2a+2+a   =41

3a+2       =41

3a           =39

      a      =13

2a+2       =(13*2)+2

              =28

so AB    =13miles

    BC     =28miles-------------->1

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part ii

As per the question , AX = 6miles

          so                  BX= 13-6 = 7miles

          from 1,            BC=28miles

                               XC= 28+7

                               XC =35 miles

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