If B is between A and C and AB =1/4(16x+24),BC=7x+15 and AC=120.Find AB and BC

Answer 1

Draw a line segment on your paper with one end being point A and the other being point C. Somewhere about halfway on the line (it doesn't really matter where) place another point and mark it point B.

Now we have split the original line segment AC into two portions, line segment AB & line segment BC. What this means is that AB and BC are two portions that, when combined, become AC.

In other words: AB + BC = AC

Now, we know that AB = 1/4(16x + 24) and that BC = 7x + 15

We also know that AC = 120

So,

_{AB BC AC}

1/4(16x+24) + 7x+15 = 120 _{Start by distributing the 1/4 to both the 16x and the 24}

4x+6 + 7x+15 = 120 _{Now, combine all the like terms}

11x+21 = 120 _{From here, isolate the variable}

11x = 99 _{Solve for x.}

x=9

Remember, we were asked to find what AB and BC were, not only to solve for x. But, we can now use x to find what AB and BC are!

So let's return to our line segments AB and BC.

All we have to do is plug in what we got for our solution to x, or 9, where we see an x in the given equations from the problem and then we're done!

AB = 1/4(16x+24)

AB = 4x+6

AB = 4(9)+6

AB= 36+6

AB=42

BC= 7x+15

BC= 7(9)+15

BC= 63+15

BC=78

^{Let's check our answers by seeing if what we got for AB and BC still add up to AC, which if you remember, was 120.}

^{AB + BC = AC}

^{AB + BC = 120}

^{42 + 78 = 120 woohoo!}

The solution to the problem is indeed: AB=42, BC=78

Answer 2

AB=1/4(16x + 24) BC= 7x +15 AC=120 B is between A and C. So AB +BC =120 and AB + 120 - BC which gives AB=120- 7x -15 = 105 - 7x so 1/4(16x +24) =4x +6 = 105 -7x and 11x = 99 x=9 so AB = 4•9 + 6 = 42 and BC =120 - 42 = 78