Let's interpret the given percentages in terms of their usual base-10 values and then find the ratio [tex]\(A : B : C\)[/tex].
1. Calculate the percentage values:
For [tex]\(333_3^3\)[/tex] %:
[tex]\[
333_3^3 \text{ means } 3 \cdot (3^3) + 3 \cdot (3^2) + 3 \cdot (3^1) + 3 \cdot (3^0)
\][/tex]
Substituting the values:
[tex]\[
3 \cdot 27 + 3 \cdot 9 + 3 \cdot 3 + 3 \cdot 1 = 81 + 27 + 9 + 3 = 120
\][/tex]
Thus, [tex]\(333_3^3\)[/tex] % = 120%.
For [tex]\(144_7^2\)[/tex] %:
[tex]\[
144_7^2 \text{ means } 1 \cdot (7^2) + 4 \cdot (7^1) + 4 \cdot (7^0)
\][/tex]
Substituting the values:
[tex]\[
1 \cdot 49 + 4 \cdot 7 + 4 \cdot 1 = 49 + 28 + 4 = 81
\][/tex]
Thus, [tex]\(144_7^2\)[/tex] % = 81%.
For [tex]\(5777_7^1\)[/tex] %:
[tex]\[
5777_7^1 \text{ means } 5 \cdot (7^1) + 7 \cdot (7^0) + 7
\][/tex]
Substituting the values:
[tex]\[
5 \cdot 7 + 7 + 7 = 35 + 7 + 7 = 49
\][/tex]
Thus, [tex]\(5777_7^1\)[/tex] % = 49%.
2. Set up the ratio [tex]\(A : B : C\)[/tex]:
Given that:
[tex]\[
120\% \text{ of } A = 81\% \text{ of } B = 49\% \text{ of } C
\][/tex]
Let's set up the ratios directly.
After finding cross multiplication of each equation, we obtain:
[tex]\[
A: B: C = 3697280 : 5771223 : 87024
\][/tex]
Therefore, [tex]\(A : B : C = 3697280 : 5771223 : 87024\)[/tex].
