Question

model 1 - eggs
chicken\t\t\tquail\t\tratio of\tratio of
number of eggs\tmass of the\tnumber of eggs\tmass of the\tnumbers of\tmasses
in the sample\tsample\t\tin the sample\tsample\teggs\teggs
1\t37.44 g\t1\t2.34 g\t1:1\t16:1
10\t10\t\t:1
438\t438\t\t:1
1 dozen\t1 dozen\t\t:1
1 million\t1 million\t\t:1

Explanation:

Step1: Calculate the mass of chicken eggs sample

For \(n = 10\) chicken eggs, since the mass of 1 chicken egg is \(m_{1}=37.44g\), the mass of 10 chicken eggs \(m_{10}=10\times37.44g = 374.4g\).
For \(n = 438\) chicken eggs, the mass of 438 chicken eggs \(m_{438}=438\times37.44g=438\times(37 + 0.44)g=438\times37g+438\times0.44g=(400 + 38)\times37g+(400+38)\times0.44g=(400\times37+38\times37)g+(400\times0.44 + 38\times0.44)g=(14800+1406)g+(176+16.72)g=16206g + 192.72g=16398.72g\).
For \(n = 1\) dozen (\(n = 12\)) chicken eggs, the mass of 12 chicken eggs \(m_{12}=12\times37.44g=(10 + 2)\times37.44g=10\times37.44g+2\times37.44g=374.4g + 74.88g=449.28g\).
For \(n = 1\) million (\(n = 10^{6}\)) chicken eggs, the mass of 1 - million chicken eggs \(m_{10^{6}}=10^{6}\times37.44g = 37440000g\).

Step2: Calculate the mass of quail eggs sample

For \(n = 10\) quail eggs, since the mass of 1 quail egg is \(m_{q1}=2.34g\), the mass of 10 quail eggs \(m_{q10}=10\times2.34g = 23.4g\).
For \(n = 438\) quail eggs, the mass of 438 quail eggs \(m_{q438}=438\times2.34g=(400 + 38)\times2.34g=400\times2.34g+38\times2.34g=936g+88.92g = 1024.92g\).
For \(n = 1\) dozen (\(n = 12\)) quail eggs, the mass of 12 quail eggs \(m_{q12}=12\times2.34g=(10 + 2)\times2.34g=10\times2.34g+2\times2.34g=23.4g+4.68g = 28.08g\).

Step3: Calculate the ratio of masses

The ratio of masses for all cases (since the ratio of numbers of eggs is \(1:1\)) is \(\frac{m_{chicken}}{m_{quail}}=\frac{37.44}{2.34}=\frac{3744}{234}=\frac{16}{1}\) (because \(37.44\div2.34 = 16\))

Answer:

Chicken		Quail		Ratio of numbers of eggs	Ratio of masses of eggs
1	\(37.44g\)	1	\(2.34g\)	\(1:1\)	\(16:1\)
10	\(374.4g\)	10	\(23.4g\)	\(1:1\)	\(16:1\)
438	\(16398.72g\)	438	\(1024.92g\)	\(1:1\)	\(16:1\)
1 dozen	\(449.28g\)	1 dozen	\(28.08g\)	\(1:1\)	\(16:1\)
1 million	\(37440000g\)	1 million	\(2340000g\)	\(1:1\)	\(16:1\)