Question

The science club is selling magazine subscriptions at \(\$ 15\) each. The club wants to raise \(\$ 315\) for science equipment. How many subscriptions does the science club need to sell to raise \(\$ 315 ?\)

Short answer

The science club needs to sell 21 subscriptions to raise $315.

Step-by-step solution

Identify the given facts

From the given exercise, it's identified that each subscription costs $15 and the club wants to raise $315.

Setup the Division

Based on the information given, the total amount the club needs to raise needs to be divided by cost of each subscription. This can be expressed mathematically as \( \frac{315}{15} \).

Perform the Division

Dividing $315 by $15 gives a result of 21.

Key concepts

Algebraic Problem Solving

Algebraic problem solving is a critical skill set in mathematics, and it involves finding unknown variables within equations. In the context of the exercise at hand, the unknown variable is the number of magazine subscriptions that the science club needs to sell. To approach this problem algebraically, we start by translating the words of the problem into a mathematical expression. Since we know that the club aims to raise \(315 and that each subscription sells for \)15, we can set up an equation:

\( x \cdot 15 = 315 \)

Here, \( x \) represents the number of subscriptions. This equation asserts that 15 dollars multiplied by the number of subscriptions will result in the total amount of money desired. Problem-solving in algebra involves manipulating these types of equations to find the value of the unknown variable.

Division in Algebra

In algebra, division is used to solve equations where the product of a known number and an unknown variable is given along with the result of that product. To isolate the variable and solve for it, division is often the necessary operation. Looking at our scenario, once we have the equation \( x \cdot 15 = 315 \), the next step is to perform algebraic division, which can also be thought of as the inverse of multiplication. We want to find out how many times 15 goes into 315. This is done by dividing the total amount \( \(315 \) by the cost per subscription \( \)15 \):

\( x = \frac{315}{15} \)

Through division in algebra, we unravel the number of times a specific quantity is contained within another, giving us a clearer picture of our variable, which in this case, signifies the necessary number of magazine subscriptions.

Mathematical Operations

Mathematical operations such as addition, subtraction, multiplication, and division are the building blocks for tackling algebraic problems. In our exercise, division is the key operation. It simplifies the relationship between the total funds needed and the price per subscription, leading us to the goal of the problem: the number of subscriptions needed. When we calculate \( 315 \div 15 \), we systematically determine how many 15s are in 315. It's essential to understand this operation beyond the mere act of calculation; it is a process that interprets how individual units amass to a total, which has practical implications in situations ranging from simple purchases to complex budgeting in finance. In essence, mathematical operations are tools that translate real-world scenarios into solvable mathematical models, enabling us to deduce logical answers from given data.