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Given the ratio [tex]\(a: b: c = 5: 3: 2\)[/tex], work out [tex]\(4a - c : 3b\)[/tex].

Give your answer in its simplest form.

Sagot :

GinnyAnswer
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]
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