if line segment AC =120ft and the ratio of line AB:line BC=3:5, what is the length of line AB ?

I set up the equation as x:120,3:5
x/120=3/5 3/120=360, 360 divided by 5=72
the answer in the book is 45, need help

It should have been x/120 = 3/8

which gives x = 45

notice AB:BC = 3:5
so AB could be 3 units, BC 5 units, making AC 8 units.

To solve this problem, you need to use a proportion since the ratio of line AB to line BC is given. Let's go through the steps:

1. Set up the proportion: We know that the ratio of AB to BC is 3:5, so we can write this as AB/BC = 3/5.

2. Plug in the given values: Given that line segment AC is 120ft, we can use this information to find BC. Since AC = AB + BC, we can substitute 120 for AC and AB gets cancelled out. Now we have (AB + BC)/BC = 3/5. Simplifying further, we get (120 + BC)/BC = 3/5.

3. Solve the proportion: Cross-multiply the ratios:
5(120 + BC) = 3BC
600 + 5BC = 3BC
600 = 3BC - 5BC
600 = -2BC
BC = -600/(-2) [Divide both sides by -2]
BC = 300ft

4. Find the length of AB: Now that we have BC, we can substitute it back into the given ratio. We know that AB:BC = 3:5, so we can write:
AB/300 = 3/5

Cross-multiply the ratios:
5AB = 3(300)
5AB = 900
AB = 900/5
AB = 180ft

Therefore, the length of line AB is 180ft. It seems like the answer in the book is incorrect.