Answer:
A:C = 3:2
Step-by-step explanation:
A:B = 7:8 is a proportion relationship and can be represented using fractions:
[tex]\displaystyle{\frac{A}{B} = \frac{7}{8}}[/tex]
Similarly the proportion relation B:C = 12:7 can be represented as:
[tex]\displaystyle{\frac{B}{C} = \frac{12}{7}}[/tex]
Multiply the first equation by the second
[tex]\displaystyle\frac{A}{B}\;\mathsf{x}\;\frac{B}{C} = \frac{7}{8}\;\mathsf{x}\;\frac{12}{7}[/tex]
This evaluates to
[tex]\displaystyle\frac{A}{C} = \frac{12}{8}[/tex]
Simplifying gives us
[tex]\displaystyle\frac{A}{C} = \frac{3}{2}[/tex]
So A:C = 3: 2
