Question

The diagram shows the route taken by a salesperson who travels from A to D via B and C. When y = x + 1, how much would the distance have been reduced by (in terms of x) if the salesperson has travelled directly from A to D and straight back to A?

Answer 1

We kinda need to know where A, B, C, and D are.

Answer 2

Okay... so redraw this diagram, except this time, replace all the y's with x+1
since
y = x+1

Answer 3

Okay, let's do that later.
Now, how much distance will the salesperson cover if he goes the long way (ie through B and C first)?

Answer 4

so the total distance travelled?

Answer 5

Yeah.. passing through B and C, before going to D.
Here's a hint... add these up

Answer 6

4x + y?

Answer 7

Very good :)
And the distance covered when the salesperson goes to D directly

is just 3y right?

Answer 8

yeap

Answer 9

Okay...
when taking the long route, the distance is 4x + y
the short route, 3y
Now replace y with x + 1

Answer 10

3(x + 1)?

Answer 11

Yeah... replace it in the 4x + y expression too

Answer 12

wait were trying to find the distance from A to D and back to A

Answer 13

yeah, it's the same concept... how much farther the distance when travelling through B and C as compared to just directly from A to D (D to A)

Answer 14

okay so pretty much were trying to find 3y + 3y?

Answer 15

No... we're trying to find the difference between
4x + y
and
3y

Answer 16

You can do that right now, too...
4x + y - 3y
Please evaluate...

Answer 17

4x + (x+1) - 3(x+1)?

Answer 18

very good.
Simplify that, and that's your answer :)

Answer 19

2x-2

Answer 20

that's it.