Problem 90 - Prealgebra

Question

You and three friends decide to rent an apartment for the academic year rather than to live in the dorms. The monthly rent is \(\$ 1250 .\) If you and your friends split the rent equally, what is your share of the monthly rent?

Step-by-Step Solution

Answer

Each person's share of the monthly rent is \(\$312.50\).

Step 1: Identify Total Monthly Rent and Number of Tenants

The total rent for the apartment is given as \( \$1250 \). This amount is to be shared among you and your three friends.

Step 2: Calculate Total Number of People Sharing the Rent

Since you and three friends are sharing the rent, the total number of people is \(1 + 3 = 4\).

Step 3: Divide Total Rent by Number of People

To find out each person's share, divide the total monthly rent of \( \$1250 \) by the number of people sharing the rent, which is 4: \[ \text{Rent per person} = \frac{1250}{4} \]

Step 4: Perform the Division

Calculate \( \frac{1250}{4} \) to determine each person's share. This results in \( \$312.50 \).

Key Concepts

Division

Division is one of the fundamental operations in arithmetic. It involves splitting a number into equal parts. For instance, if you want to divide a pizza among friends, division helps determine how much each person gets. Division is represented by the symbol "/" or as a fraction bar.To perform division, you have a dividend (the number you are dividing) and a divisor (the number you are dividing by). The result of division is called the quotient. In the exercise, the dividend is the total rent amount, \(\\(1250\), and the divisor is the number of people sharing the rent, which is 4. The division can be expressed as:\[\text{Rent per person} = \frac{1250}{4}\]To solve, you calculate how many times the divisor fits into the dividend, which results in each friend's share being \(\\)312.50\). Simple division is extremely useful in everyday tasks, making it essential to grasp.

Word Problems

Word problems require translating a written scenario into a mathematical expression or operation that allows you to find a solution. Identifying key information is crucial to convert the situation into a math problem. Here, the word problem involves sharing rent. The scenario mentions you and three friends, pointing towards division since it's about equal sharing. Key steps to tackle word problems:

• Read the problem carefully to understand what is being asked.
• Identify relevant numbers and what they represent, such as total rent and number of friends.
• Determine the arithmetic operation required—here, it's division to split the cost.
• Translate into a math equation and solve.

Word problems are practical applications of math concepts. They build critical thinking by requiring you to decide the best approach based on the given information.

Cost Sharing

Cost sharing is a situation where individuals divide a total expense equally among a group. It is common in scenarios like renting an apartment, sharing a meal, or splitting a cab fare.In the exercise, cost sharing involves dividing \(\$1250\) equally among four people. Here's how you can think about it:

• Identify the total cost: This is the expense that needs splitting—in this case, the rent.
• Count the number of sharers: You and three friends make four people in total.
• Divide the total by the number of sharers: This represents each person's share.

Cost sharing simplifies managing joint expenses and ensures fairness when multiple people are benefitting from a shared resource. It turns a potentially complex calculation into manageable arithmetic, promoting easy collaboration when dealing with group expenditures.