Understanding Beautician's Income Components
A beautician's total income is composed of her salary and the tips she receives.
Relating Tips to Salary
The problem states that the tips were $\frac{5}{4}$ of her salary. Let $S$ represent the salary.
- Salary = $S$
- Tips = $\frac{5}{4} S$
Calculating Total Income
Total income is the sum of salary and tips.
- Total Income = Salary + Tips
- Total Income = $S + \frac{5}{4} S$
- Combine terms using a common denominator ($S = \frac{4}{4} S$):
- Total Income = $\frac{4}{4} S + \frac{5}{4} S = \frac{4+5}{4} S = \frac{9}{4} S$
Determining the Fraction from Tips
To find the fraction of income from tips, divide the tips amount by the total income.
- Fraction from Tips = $\frac{\text{Tips}}{\text{Total Income}}$
- Fraction from Tips = $\frac{\frac{5}{4} S}{\frac{9}{4} S}$
- The $S$ terms cancel out:
- Fraction from Tips = $\frac{5/4}{9/4}$
- Simplify the compound fraction: $\frac{5}{4} \times \frac{4}{9} = \frac{5}{9}$
Thus, $\frac{5}{9}$ of the beautician's income came from tips.
Similar Questions
- $1.236576576...$
can be written in the form of: - What is the sum of $\frac{1}{3}$, $\frac{4}{3}$ and $\frac{3}{4}$?
- Four persons A, B, C and D completed a task in $\frac{2}{3} \text{ h}, \frac{3}{4} \text{ h}, \frac{4}{5} \text{ h}$ and $\frac{1}{5} \text{ h}$ respectively. Who among the following took the highest amount of time to complete the task?
- The value of $\frac{4}{3} + \left( \frac{1}{1 + \frac{5}{6}} \right) - \frac{5}{4}$ is
What is the value of
$\frac{7}{9} - \frac{11}{12} + \frac{13}{16} - \frac{1}{8}$?
- How much does one need to add to $\frac{1}{2}$ to get $2$?
- The sum of the numerator and denominator of a fraction is 11. If the numerator is decreased by 1, the fraction becomes $\frac{1}{4}$. Find the fraction.
- If the numerator of a fraction is increased by 30% and its denominator is decreased by 35%, the value of the fraction becomes $\frac{3}{15}$. Find the original fraction.
- Two-fifth of seven-seventeenth of three-fifth of a number is 84. Find 40% of that number.
- What smallest fraction should be added to $3\frac{2}{3} + 6\frac{7}{12} + 4\frac{9}{36} + 5 + 7\frac{1}{12}$ to make the sum a whole number?
Important Questions from Fractions
5 \(\frac{3}{4}\) + x + 2 \(\frac{1}{2}\) = 10 \(\frac{1}{8}\) Find the value of x.
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
Number 0.232323 can be written in rational form as:
Solve: \(\frac{1}{2}\) [{-2(2 + 3)*20}/2]
Match the following.
Column I
Column II
a.
Equivalent fraction of \(\frac{7}{12}\) is
i.
Proper fraction
b.
Equivalent fraction of \(\frac{9}{15}\) is
ii.
Improper fraction
c.
\(\frac{7}{11}\) is
iii.
\(\frac{21}{36}\)
d.
\(\frac{19}{5}\) is
iv.
\(\frac{3}{5}\)
