Problem 47 - Prealgebra

Question

Find each number. PERSONAL CARE In nine visits to the styling salon, Andre had spent \(\$ 169\) for haircuts. Of that amount, \(\$ 16\) was in tips. Write and solve an equation to find how much Andre pays for each haircut before the tip.

Step-by-Step Solution

Answer

Andre pays $17 per haircut before the tip.

Step 1: Understand the Problem

Andre has visited the salon nine times and spent a total of $169. Included in this amount is $16 for tips. We need to determine how much Andre paid for each haircut before tips.

Step 2: Set Up the Equation

To find out how much Andre pays per haircut (without tips), we first subtract the total tip amount from the total cost. This gives the total cost for haircuts without tips. We then divide this result by the number of visits to find the cost per haircut. Let the cost of each haircut be represented by \( x \). The equation becomes: \( 9x = 169 - 16 \).

Step 3: Simplify the Equation

First, calculate the total cost of haircuts without tips: \( 169 - 16 = 153 \). Substitute this back into the equation: \( 9x = 153 \).

Step 4: Solve the Equation

To find the value of \( x \), divide both sides of the equation by 9: \( x = \frac{153}{9} \).

Step 5: Calculate the Solution

Calculate \( \frac{153}{9} \) which equals 17. Thus, the cost per haircut before tips is $17.

Key Concepts

Word Problems

Word problems can seem daunting at first, but they are just stories with numbers. In this exercise, we have the story of Andre's visits to the salon. To solve any word problem, the key is to first break down the information and organize it.

• Identify what's given: Andre made nine visits and spent a total of $169, including $16 in tips.
• Determine what you need to find: The cost of each haircut before tips.
• Translate the problem into mathematical expressions using equations.

By carefully picking out these details and setting up the right equations, word problems become much more manageable and even fun to solve! Remember, the goal is to relate the narrative to mathematical operations.

Prealgebra

Prealgebra involves understanding how to manipulate numbers and basic operations. It often deals with setting up equations that represent real-world situations, just like Andre's salon visits.

• Learn to define variables for unknowns. In this case, we define variable "x" for the cost of each haircut before tip.
• Practice rearranging and solving equations: for Andre, the equation yields from subtracting the tip from the total and isolating the variable.
• Understand operations such as addition and subtraction within the problem's context.

In this problem, prealgebra skills help to transition from words to numbers, as granting the scenario a structure enables a clear path to the solution.

Basic Arithmetic Operations

Basic arithmetic operations like addition, subtraction, multiplication, and division are fundamental in solving equations. Let's see how they fit into this situation.

• Subtraction: Starting with removing the tips from the total cost. This gives us the amount spent purely on haircuts.
• Division: Once we have the total haircut cost, this operation helps distribute it equally among the nine visits.
• Calculation: Perform \( 169 - 16 = 153 \) to find the nontip total, and then \( 153 \div 9 = 17 \), solving for each haircut's cost.

Through basic arithmetic operations, students can confidently navigate a variety of numerical challenges, vital for successfully solving real-life problems like Andre’s spending at the salon. These operations are the building blocks of future math problems.