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Select the best answer for the question:

A family spends [tex]\frac{1}{10}[/tex] of its annual income for housing, [tex]\frac{1}{4}[/tex] for food and clothing, [tex]\frac{1}{5}[/tex] for general expenses, and [tex]\frac{2}{15}[/tex] for entertainment. What fractional part of their income is spent on these items altogether?

A. [tex]\frac{1}{7}[/tex]

B. [tex]\frac{5}{41}[/tex]

C. [tex]\frac{11}{12}[/tex]

D. [tex]\frac{41}{60}[/tex]


Sagot :

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]
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