Question

You take home \(\$ 400\) a month from your part-time job as a cashier. Each month you budget \(\$ 120\) for car expenses, \(\$ 160\) for food, and the rest for entertainment. a. What fraction of your take-home pay is budgeted for car expenses? b. What fraction of your take-home pay is budgeted for food? c. What fraction of your take-home pay is budgeted for entertainment?

Short answer

Answer: The fractions of monthly take-home pay budgeted for each category are: a. Car expenses: \(\frac{3}{10}\) b. Food expenses: \(\frac{2}{5}\) c. Entertainment expenses: \(\frac{3}{10}\)

Step-by-step solution

Calculate the fraction for car expenses.

To find the fraction of take-home pay budgeted for car expenses, divide the amount budgeted for car expenses by the total take-home pay: \(\frac{120}{400}\). Simplify this fraction, and you get \(\frac{3}{10}\).

Calculate the fraction for food expenses.

To find the fraction of take-home pay budgeted for food expenses, divide the amount budgeted for food expenses by the total take-home pay: \(\frac{160}{400}\). Simplify this fraction, and you get \(\frac{2}{5}\).

Calculate the total amount spent on car and food expenses.

Add the amounts budgeted for car and food expenses together: \(120 + 160 = 280\).

Calculate the amount budgeted for entertainment.

Subtract the amount spent on car and food expenses from the total take-home pay to find the amount budgeted for entertainment: \(400 - 280 = 120\).

Calculate the fraction for entertainment expenses.

To find the fraction of take-home pay budgeted for entertainment expenses, divide the amount budgeted for entertainment expenses by the total take-home pay: \(\frac{120}{400}\). Simplify this fraction, and you get \(\frac{3}{10}\). Now we have found the fractions for each category of expenses: a. The fraction of take-home pay budgeted for car expenses is \(\frac{3}{10}\). b. The fraction of take-home pay budgeted for food expenses is \(\frac{2}{5}\). c. The fraction of take-home pay budgeted for entertainment expenses is \(\frac{3}{10}\).