Given:
[tex]\[ \triangle Q \ 1 \ 0 \][/tex]

If [tex]$ 333_3^3 \% $[/tex] of [tex]$ A = 144_7^2 \% $[/tex] of [tex]$ B = 5777_7^1 \% $[/tex] of [tex]$ C $[/tex], then find [tex]$ A : B : C $[/tex].

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].

Given: [tex]\[ \triangle Q \ 1 \ 0 \][/tex]If [tex]\( 333_3^3 \% \)[/tex] of [tex]\( A = 144_7^2 \% \)[/tex] of [tex]\( B = 5777_7^1 \% \)[/tex] of [tex]\( C \)[/tex], then find [tex]\( A : B : C \)[/tex].

Answer :

Other Questions

Given:
[tex]\[ \triangle Q \ 1 \ 0 \][/tex]

If [tex]\( 333_3^3 \% \)[/tex] of [tex]\( A = 144_7^2 \% \)[/tex] of [tex]\( B = 5777_7^1 \% \)[/tex] of [tex]\( C \)[/tex], then find [tex]\( A : B : C \)[/tex].