Question

in a particular country, for men born in 1940 the predicted years of receiving retirement benefits is 17.4 for the bottom 10% of income earners versus 29.6 years for the top 10%.
answer parts (a) through (d) below.
...
quantity to 1.
the scaled ratio is 1.70 : 1.
(type integers or decimals rounded to two decimal places as needed.)
(b) fill in the blanks.
a man born in 1940 from the top 10% will receive retirement benefits for 1.70 times as many years as a man from the bottom 10%.
(c) compute the ratio of predicted years of receiving retirement benefits for the bottom 10% to the top 10% and scale the second quantity to 100.
\square : \square
(type integers or decimals rounded to one decimal place as needed.)

Explanation:

Step1: Set up the ratio

The ratio of the bottom 10% to the top 10% is \(\frac{17.4}{29.6}\).

Step2: Scale the second quantity to 100

Let the ratio be \(x:100\). We know that \(\frac{17.4}{29.6}=\frac{x}{100}\). Cross - multiply: \(29.6x = 17.4\times100\), so \(x=\frac{17.4\times100}{29.6}\).

Step3: Calculate the value of \(x\)

\(x=\frac{1740}{29.6}\approx58.8\)

Answer:

\(58.8:100\)