Problem 51 - Prealgebra

Question

Suppose Benito is selling 10 of his music CDs on the Internet, and it costs \(\$ 1.25\) per CD to send them to a buyer. If he decides to sell each CD for the same price \(p,\) which expression would you use to find how much money he will receive after sending all 10 CDs? F \(22.75 p\) G \(22.5 p-10\) H \(10+1.25\) J \(10 p-12.5\)

Step-by-Step Solution

Answer

The expression is \(10p - 12.5\), which is option J.

Step 1: Determine Total Revenue from Selling CDs

First, calculate how much money Benito receives from selling the CDs. Since each CD is sold at a price \( p \), the total revenue from selling 10 CDs is \( 10p \).

Step 2: Compute Shipping Costs

Next, calculate the total cost for shipping all the CDs. With a shipping cost of \( \$1.25 \) per CD and 10 CDs to ship, the shipping cost is \( 10 \times 1.25 = 12.5 \).

Step 3: Calculate Net Earnings

To find out the net earnings, subtract the total shipping cost from the total revenue. This gives the equation: \( 10p - 12.5 \).

Step 4: Compare with Provided Options

Compare the expression we've calculated, \( 10p - 12.5 \), with the provided options. Option J matches this expression exactly.

Key Concepts

Algebraic expressions

In prealgebra, an algebraic expression is a mathematical phrase containing numbers, variables, and operations. Understanding algebraic expressions is vital as it forms the basis of algebra and helps solve various problems. For instance, Benito’s CD selling scenario involves creating an expression that includes a variable and mathematical operations. Here, the variable is \( p \), representing the price of each CD. To find the total earnings from the sale, we use the expression \( 10p \). This means you multiply the number of CDs by the price per CD, which is a typical use of algebraic expressions in real-world problems. Algebraic expressions enable us to form equations crucial for making calculations and predictions.

Word problems

Word problems can sometimes be tricky, but they are just math in disguise, describing everyday situations. In a word problem, you figure out the needed operation by picking out keywords and phrases. With Benito's CDs, the problem describes a selling situation and asks for a method to calculate earnings after costs. The essential skill here is translation—turning words into equations. Look for what you need to find, like the net earnings after shipping. Understand the whole context to grasp what operations to use on the numbers and variables given. Practicing word problems boosts critical thinking skills, making mathematical concepts more tangible.

Cost calculations

Cost calculations are a fundamental part of many math problems, especially those involving business scenarios and personal finance. In Benito's case, cost calculations involve both revenue and expenses. The income comes from selling the CDs, calculated by \( 10p \) since each CD sells for \( p \). We also have costs, specifically the shipping cost where each CD costs \$1.25 to ship, resulting in a total expense of \( 10 \times 1.25 = 12.5 \). The key to cost calculations is understanding how to correctly sum up expenses and how they affect profits. The final solution requires subtracting these expenses from total income to find net earnings, which in this problem is represented by the expression \( 10p - 12.5 \). Understanding cost calculations ensures accurate financial planning and decision-making in any selling context.