/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 40 A small copy shop spent \(24 \%\... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

A small copy shop spent \(24 \%\) of its monthly revenue on supplies, \(17 \%\) on renting the building, and \(33 \%\) on payroll and taxes. If after paying these expenses, $$\$ 7,384$$ dollars in profit is left, then how much did the copy shop spend on rent? A. $$\$ 3,976$$ B. $$\$ 4,828$$ C. $$\$ 19,198$$ D. $$\$ 28,400$$

Short Answer

Expert verified
The copy shop spent $$\$ 4,828$$ on rent. Answer: (B).

Step by step solution

01

Determine the expense percentages

The exercise provides us with the expense percentages for supplies, rent, and payroll/taxes: - Supplies: \(24 \%\) - Rent: \(17 \%\) - Payroll and Taxes: \(33 \%\)
02

Calculate the non-expense percentage

We'll find the percentage of money that is not used as an expense, which results in the profit. To do this, simply subtract the given expense percentages from \(100 \%\): Non-expense percentage (Profit) = \(100 \% - 24 \% - 17 \% - 33 \% = 26 \%\)
03

Calculate the total revenue

As the profit is $$\$ 7,384$$ and this represents \(26 \%\) of the total revenue, we can now calculate the total revenue by using the following formula: Revenue = Profit / Profit percentage Revenue = $$\$ 7,384 / 0.26$$ Revenue = $$\$ 28,400$$
04

Calculate the rent expense

Now that we have the total revenue, we can calculate the rent expense by multiplying the rent percentage with the total revenue: Rent Expense = Rent percentage * Total revenue Rent Expense = $0.17 * $$\$ 28,400$$ Rent Expense = $$\$ 4,828$$ So, the copy shop spent $$\$ 4,828$$ on rent. The correct answer is (B).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Percentage Calculations
Understanding percentages is a fundamental skill in math, especially when handling real-world problems like budgeting or analyzing data. A percentage represents a fraction of 100 and is often used to compare proportions. For instance, if a small business spends a certain percentage of its revenue on different expenses, you need to calculate each of these amounts to understand where the money goes.

In our copy shop example, the percentages for supplies, rent, and payroll are given, and the task is to find the actual amounts these percentages represent. To do so, we need to know the total revenue, which can be reverse-calculated from the profit, represented by the remainder percentage after all expenses. Once the total revenue is found, simply multiply it by the percentage of each expense to get the actual amounts. This practical application of percentage calculations is crucial, and mastering this can help students in many real-life situations.
Profit Calculation
Profit calculation is a vital concept not just in mathematics, but in the world of business and finance. Profit is essentially what's leftover once all expenses have been subtracted from the total revenue. In mathematical terms, it's a matter of understanding how to work backwards from a percentage figure and apply it to find a whole number.

For our GED problem, we know the profit represents 26% of the total revenue—this percentage is what remains after expenses for supplies, rent, and payroll are accounted for. To calculate the shop's expenses, we first calculate the total revenue by dividing the profit by its percentage (26%). This kind of problem emphasizes the importance of isolating variables and solving for the unknown—a process that is very common in algebra and business arithmetic. By grasping profit calculation, students gain insights into not only how to solve textbook problems but also how to manage financial aspects of running a business.
GED Test Preparation
Preparing for the GED test requires a comprehensive study plan that includes understanding key mathematical concepts like percentage calculations and profit calculation. Since the GED test aims to award a certification equivalent to a high school diploma, it encompasses a range of subjects with math being a significant component. As you prepare, focus on learning how to solve different types of math problems systematically.

Start by familiarizing yourself with the types of math problems that commonly appear on the test, such as those involving percentages, profit, and basic algebra. Practice solving these problems step by step and understand the rationale behind each step. Use resources like textbooks, educational platforms, or GED prep courses to fortify your grasp of these topics. Remember that the GED math test measures your critical thinking and problem-solving skills as much as it does your mathematical knowledge. Therefore, aim to understand concepts deeply rather than just memorizing formulas. By doing so, you'll not only be better prepared for the GED test but also develop a solid foundation for future mathematical learning and everyday financial decision-making.

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