Certainly! Let's solve the problem step-by-step with the given ratios [tex]\( a:b:c = 5:3:2 \)[/tex].
1. Substituting Individual Values:
- Given [tex]\( a = 5 \)[/tex], [tex]\( b = 3 \)[/tex], and [tex]\( c = 2 \)[/tex].
2. Calculate [tex]\( 4a - c \)[/tex]:
[tex]\[
4a - c = 4(5) - 2 = 20 - 2 = 18
\][/tex]
3. Calculate [tex]\( 3b \)[/tex]:
[tex]\[
3b = 3(3) = 9
\][/tex]
4. Form the Ratio [tex]\( 4a - c : 3b \)[/tex]:
So, we have the ratio:
[tex]\[
18 : 9
\][/tex]
5. Simplify the Ratio:
- Find the greatest common divisor (GCD) of 18 and 9, which is 9.
- Divide both terms of the ratio by their GCD:
[tex]\[
\frac{18}{9} : \frac{9}{9} = 2 : 1
\][/tex]
Thus, the simplest form of the ratio [tex]\( 4a - c : 3b \)[/tex] is [tex]\( 2 : 1 \)[/tex].
So, the answer is:
[tex]\[
2 : 1
\][/tex]
