https://file.aiquickdraw.com/mathbot/file/1730749078760xrakafnj.jpg

To solve this problem, let's define two variables based on the information given:

- Let $ x $ be the number of tee shirts bought.
- Let $ y $ be the number of long sleeve shirts bought.

From the problem, we have two key pieces of information:

1. **Total number of shirts:** She bought a total of 10 shirts.
   \[
   x + y = 10
   \]

2. **Total cost of shirts:** She spent $66 in total. Tee shirts cost $7 each, and long sleeve shirts cost $6 each.
   \[
   7x + 6y = 66
   \]

### Solving the Equations

#### Step 1: Solve for one variable in terms of the other from the first equation
From $ x + y = 10 $, we can express $ y $ in terms of $ x $:
\[
y = 10 - x
\]

#### Step 2: Substitute $ y $ in the second equation
Now substitute $ y = 10 - x $ into the cost equation:
\[
7x + 6(10 - x) = 66
\]

#### Step 3: Simplify and solve for $ x $
Expanding and simplifying:
\[
7x + 60 - 6x = 66
\]
\[
x + 60 = 66
\]
\[
x = 6
\]

#### Step 4: Find $ y $ using $ x = 6 $
Substitute $ x = 6 $ back into the equation $ y = 10 - x $:
\[
y = 10 - 6 = 4
\]

### Solution
Lisa bought:
- **6 tee shirts** (at $7 each)
- **4 long sleeve shirts** (at $6 each)

These satisfy both the total cost and the total number of shirts.

Let me know if you would like a further breakdown or have questions.

---

Here are 5 related questions to practice:

1. If Lisa spent $80 instead, how many of each type of shirt could she buy?
2. What if the cost of tee shirts changed to $8? How would that affect the solution?
3. Suppose Lisa bought 12 shirts with the same price per shirt. How many of each would she have bought for $66?
4. If Lisa had a $100 budget but wanted to buy at least 5 of each shirt type, how would you set up the equations?
5. How would the solution change if long sleeve shirts cost $5 each?

**Tip:** When setting up problems with two unknowns, use clear labels for variables and translate the conditions into equations.

Lisa spent $66 on shirts. Tee shirts cost $7 and long sleeve shirts cost $6. If she bought a total of 10, then how many shirts of each kind did she buy?

Learn how to solve a system of equations to determine the number of tee shirts and long sleeve shirts Lisa bought. This problem involves setting up and solving linear equations based on given conditions, suitable for students in Grades 6-8.

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