Question

Andrea, Ben, Christine, and Doug all live on the same street as their school. The street runs from east to west.Andrea lives 5 1/2 blocks to the west of school.Ben lives 4 blocks to the east of school.Christine lives 2 blocks to the west of school.Doug lives 6 1/2 blocks to the east of school.Use this information to complete the following.Part ARepresent the relative position of the houses on a number line with the school at zero, points to the west represented by negative numbers, and points to the east represented by positive numbers.Part BHow far does Ben live from Andrea? Show how you arrived at your answer using sums or differences.

Answer 1

From the statement of the problem, we know that.

• Andrea lives 5 1/2 blocks to the west of school → x = -5.5,

,

• Ben lives 4 blocks to the east of school → x = +4,

,

• Christine lives 2 blocks to the west of school → x = -2,

,

• Doug lives 6 1/2 blocks to the east of school → x = +6.5.

A) Using the data above, we have:

B) The x coordinate of:

• Andrea is x_A = -5.5,

,

• Ben is x_B = +4.

The distance between Ben and Andrea is equal to the difference between its coordinates:

$d=x_B-x_A=4-(-5.5)=4+5.5=9.5.$

We find that Ben lives 9.5 blocks from Andrea.