Question

which of the following choices shows the simplified ratio of 15 feet : 210 feet?
1 ft : 14 ft
3 ft : 70 ft
5 ft : 70 ft
none of the choices are correct

Explanation:

Step1: Simplify the ratio

To simplify the ratio \(15\) feet : \(210\) feet, we divide both parts by their greatest common divisor (GCD). The GCD of \(15\) and \(210\) is \(15\). So, \(\frac{15}{15}:\frac{210}{15}=1:14\) (in feet).

Step2: Compare with options

Now we check the options:

• First option: \(1\) ft : \(14\) ft, which matches our simplified ratio.
• Second option: \(3\) ft : \(70\) ft, \(\frac{3}{70}

eq\frac{1}{14}\) (since \(1\times70 = 70\), \(14\times3 = 42\), \(70
eq42\)).

• Third option: \(5\) ft : \(70\) ft, \(\frac{5}{70}=\frac{1}{14}\)? Wait, \(\frac{5}{70}=\frac{1}{14}\) (dividing numerator and denominator by \(5\)), but wait no, wait our simplified ratio is \(1:14\), and \(5:70\) simplifies to \(1:14\) as well? Wait no, wait \(15:210\) simplifies to \(1:14\) (dividing by \(15\)), and \(5:70\) is dividing by \(5\) to get \(1:14\) too? Wait no, wait \(15\div15 = 1\), \(210\div15 = 14\). \(5\div5 = 1\), \(70\div5 = 14\). Wait but the first option is \(1:14\), which is also correct. Wait maybe I made a mistake. Wait the first option is \(1\) ft : \(14\) ft, which is exactly the simplified ratio of \(15:210\) (since \(15\div15 = 1\), \(210\div15 = 14\)). So the first option is correct.

Answer:

A. \(1\) ft : \(14\) ft (assuming the first option's identifier is A, as per the typical multiple - choice setup with radio buttons. If the first option is labeled with the first radio button, then the answer is the first option: \(1\) ft : \(14\) ft)