Question

select the correct answer.
a plastic bin contains red, yellow, and green key chains. out of 350 key chains, 10% percent are yellow. of the remaining key chains, \\(\frac{3}{5}\\) are green. how many red key chains are inside the bin?
\\(\bigcirc\\) a. 26
\\(\bigcirc\\) b. 35
\\(\bigcirc\\) c. 126
\\(\bigcirc\\) d. 189

Explanation:

Step1: Calculate the number of yellow key - chains

The number of yellow key - chains is \(10\%\) of \(350\). Using the formula \(n = p\times N\) (where \(p = 0.1\) and \(N = 350\)), we have \(n_{yellow}=0.1\times350 = 35\).

Step2: Calculate the number of non - yellow key - chains

The number of non - yellow key - chains is \(N_{non - yellow}=350 - 35=315\).

Step3: Calculate the proportion of red key - chains among non - yellow key - chains

Since the proportion of green key - chains among non - yellow key - chains is \(\frac{3}{5}\), the proportion of red key - chains among non - yellow key - chains is \(1-\frac{3}{5}=\frac{2}{5}\).

Step4: Calculate the number of red key - chains

Using the formula \(n = p\times N\) (where \(p=\frac{2}{5}\) and \(N = 315\)), we have \(n_{red}=\frac{2}{5}\times315=\frac{2\times315}{5}=2\times63 = 126\).

Answer:

C. 126