Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 then how many of each kind did she buy?  

Let's define the variables:
- Let $ x $ represent the number of fancy shirts Kristin bought.
- Let $ y $ represent the number of plain shirts she bought.

We are given two pieces of information:
1. She bought a total of 7 shirts:  
   \[
   x + y = 7
   \]
2. She spent a total of $131, with fancy shirts costing $28 and plain shirts costing $15:  
   \[
   28x + 15y = 131
   \]

Now, we can solve this system of equations.

### Step 1: Solve the first equation for one variable
From the equation $ x + y = 7 $, solve for $ y $:
\[
y = 7 - x
\]

### Step 2: Substitute into the second equation
Substitute $ y = 7 - x $ into the second equation $ 28x + 15y = 131 $:
\[
28x + 15(7 - x) = 131
\]
Simplify the equation:
\[
28x + 105 - 15x = 131
\]
Combine like terms:
\[
13x + 105 = 131
\]
Subtract 105 from both sides:
\[
13x = 26
\]
Solve for $ x $:
\[
x = 2
\]

### Step 3: Find $ y $
Now that we know $ x = 2 $, substitute it into $ y = 7 - x $:
\[
y = 7 - 2 = 5
\]

### Conclusion:
Kristin bought 2 fancy shirts and 5 plain shirts.

Would you like further explanation or details? Here are some related questions to consider:

1. How can you verify that these values satisfy both original equations?
2. What if Kristin had spent $150 instead, but still bought 7 shirts?
3. How would the problem change if fancy shirts were $30 instead of $28?
4. What is the general approach to solving systems of equations like this one?
5. Can we solve this problem using a graphing method instead of substitution?

**Tip:** When solving systems of equations, substitution or elimination methods work well for small systems, while graphing or matrix methods may be useful for larger systems.

Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7, how many of each kind did she buy?

Learn how to solve a system of equations where Kristin spends $131 on 7 shirts, with fancy shirts costing $28 and plain shirts costing $15. This step-by-step solution demonstrates the substitution method and is suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation