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### Problem:
Two friends, Sarah and Mike, went shopping. Sarah bought 3 shirts and 2 pants for a total of $160. Mike bought 2 shirts and 3 pants for a total of $170. Find the cost of one shirt and one pair of pants.

### Step-by-Step Solution:

Let:
- $ x $ = the cost of one shirt
- $ y $ = the cost of one pair of pants

We can create the following system of linear equations based on the given information:

1. $ 3x + 2y = 160 $  (Sarah's purchase)
2. $ 2x + 3y = 170 $  (Mike's purchase)

#### Step 1: Solve one of the equations for one variable
We'll solve the first equation for $ x $ in terms of $ y $:

\[ 3x + 2y = 160 \]
\[ 3x = 160 - 2y \]
\[ x = \frac{160 - 2y}{3} \]

#### Step 2: Substitute into the second equation
Now substitute this expression for $ x $ into the second equation $ 2x + 3y = 170 $:

\[ 2\left(\frac{160 - 2y}{3}\right) + 3y = 170 \]

#### Step 3: Solve for $ y $
To eliminate the fraction, multiply everything by 3:

\[ 2(160 - 2y) + 9y = 510 \]
\[ 320 - 4y + 9y = 510 \]
\[ 320 + 5y = 510 \]
\[ 5y = 510 - 320 \]
\[ 5y = 190 \]
\[ y = \frac{190}{5} \]
\[ y = 38 \]

So, the cost of one pair of pants is **$38**.

#### Step 4: Substitute $ y = 38 $ into the equation for $ x $
Now substitute $ y = 38 $ into the equation $ x = \frac{160 - 2y}{3} $:

\[ x = \frac{160 - 2(38)}{3} \]
\[ x = \frac{160 - 76}{3} \]
\[ x = \frac{84}{3} \]
\[ x = 28 \]

So, the cost of one shirt is **$28**.

### Final Answer:
- The cost of one shirt is **$28**.
- The cost of one pair of pants is **$38**.

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Here are 5 related problems for further practice:
1. Two people go shopping and purchase different quantities of items. Can you create a system of equations to solve for the individual item prices?
2. Solve the system of equations $ 4x + 3y = 120 $ and $ 5x + 2y = 130 $.
3. If the price of one pen is $2 more than a pencil and buying 3 pens and 4 pencils costs $20, how much does each cost?
4. You buy 5 apples and 3 bananas for $8, and your friend buys 2 apples and 6 bananas for $10. Find the price of each.
5. Solve the system: $ 7x + 5y = 90 $ and $ 6x + 4y = 80 $.

**Tip**: When solving a system of equations, the substitution method is helpful when one equation is easily solved for one variable. Otherwise, elimination might be more efficient.

Find the cost of one shirt and one pair of pants by solving a system of linear equations in two variables. Sarah bought 3 shirts and 2 pants for $160, while Mike bought 2 shirts and 3 pants for $170. This problem illustrates how to use substitution method to find the individual costs. Suitable for Grades 8-10.

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