To find out what fractional part of their income is spent on the given categories, we'll add up the fractions representing each category: housing, food and clothing, general expenses, and entertainment.
The given fractions are:
- Housing: [tex]\(\frac{1}{10}\)[/tex]
- Food and clothing: [tex]\(\frac{1}{4}\)[/tex]
- General expenses: [tex]\(\frac{1}{5}\)[/tex]
- Entertainment: [tex]\(\frac{2}{15}\)[/tex]
To add these fractions, we typically need a common denominator. However, since we already know the exact totals from provided information, let's confirm the total part of income spent on these items:
The fractions in decimal form are:
- Housing: [tex]\(0.1\)[/tex]
- Food and clothing: [tex]\(0.25\)[/tex]
- General expenses: [tex]\(0.2\)[/tex]
- Entertainment: [tex]\(0.1333...\)[/tex] (approximately)
Adding these together:
[tex]\(0.1 + 0.25 + 0.2 + 0.1333... = 0.6833...\)[/tex]
Converting [tex]\(0.6833...\)[/tex] back to a fraction, it's approximately [tex]\( \frac{41}{60} \)[/tex].
Thus, the total fraction of their income spent on these categories is [tex]\(\frac{41}{60}\)[/tex].
The best answer, given the choices, is:
D. [tex]\( \frac{41}{60} \)[/tex]
