Let's solve the given problem step-by-step.
1. Identify the known information:
- The total length of [tex]\( AB \)[/tex] is 18 cm.
- Let [tex]\( AC \)[/tex] be the distance from [tex]\( A \)[/tex] to [tex]\( C \)[/tex].
- Let [tex]\( CB \)[/tex] be the distance from [tex]\( C \)[/tex] to [tex]\( B \)[/tex].
- We are given that [tex]\( AC \)[/tex] is 3 cm shorter than [tex]\( CB \)[/tex].
2. Establish relationships based on the information given:
- We can denote the distance [tex]\( AC \)[/tex] as [tex]\( x \)[/tex] cm.
- Since [tex]\( AC \)[/tex] is 3 cm shorter than [tex]\( CB \)[/tex], we can write [tex]\( CB \)[/tex] as [tex]\( x + 3 \)[/tex] cm.
- The sum of [tex]\( AC \)[/tex] and [tex]\( CB \)[/tex] is equal to the length of [tex]\( AB \)[/tex]. So, [tex]\( x + (x + 3) = 18 \)[/tex].
3. Set up the equation:
- From the relationship above:
[tex]\[
x + (x + 3) = 18
\][/tex]
- Simplify the equation:
[tex]\[
2x + 3 = 18
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
- Subtract 3 from both sides:
[tex]\[
2x = 15
\][/tex]
- Divide both sides by 2:
[tex]\[
x = 7.5
\][/tex]
5. Calculate [tex]\( CB \)[/tex]:
- Since [tex]\( CB = x + 3 \)[/tex]:
[tex]\[
CB = 7.5 + 3 = 10.5
\][/tex]
So, the distances are:
[tex]\[
AC = 7.5 \, \text{cm}
\][/tex]
[tex]\[
CB = 10.5 \, \text{cm}
\][/tex]
Therefore, the lengths are:
[tex]\[
AC = 7.5 \, \text{cm}, \quad CB = 10.5 \, \text{cm}
\][/tex]
