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The problem involves Edward's income, which is modeled by the equation:

\[
I = 100 + 12J + 5T + 7S + 5H - 8M
\]

where:
- $ I $ is Edward's total income.
- $ J $ is the number of jeans he sells.
- $ T $ is the number of T-shirts he sells.
- $ S $ is the number of shorts he sells.
- $ H $ is the number of hats he sells.
- $ M $ is the number of meals he buys.

Given the following:
- Edward's income $ I = 197 $ dollars.
- He sells 5 pairs of jeans $ J = 5 $.
- He sells 5 T-shirts $ T = 5 $.
- He sells 3 hats $ H = 3 $.
- He buys 3 meals $ M = 3 $.

We need to find how many pairs of shorts Edward sold, i.e., solve for $ S $.

### Step 1: Plug in the known values into the equation

\[
197 = 100 + 12(5) + 5(5) + 7S + 5(3) - 8(3)
\]

### Step 2: Simplify the equation

First, calculate each term:
- $ 12(5) = 60 $
- $ 5(5) = 25 $
- $ 5(3) = 15 $
- $ 8(3) = 24 $

Substitute these into the equation:

\[
197 = 100 + 60 + 25 + 7S + 15 - 24
\]

Now simplify the constants:

\[
197 = 176 + 7S
\]

### Step 3: Solve for $ S $

\[
197 - 176 = 7S
\]
\[
21 = 7S
\]
\[
S = \frac{21}{7} = 3
\]

So, Edward sold **3 pairs of shorts**.

---

Would you like more details or have any other questions? Here are 5 related questions to explore:

1. What happens to Edward's income if he buys more meals but sells the same amount of clothes?
2. If Edward sells no jeans, how many more T-shirts would he need to sell to maintain the same income?
3. How would Edward's income change if he received a flat bonus of $50 per week?
4. What if the cost of meals increases and he has to pay $10 per meal? How would that affect his income?
5. How many pairs of jeans would Edward need to sell if he doesn't sell any hats?

**Tip:** Always isolate the variable you're solving for to avoid errors in multi-variable equations.

Edward works at a clothing store, and works on commission. His income can be modeled by the following equation: I = 100 + 12J + 5T + 7S + 5H - 8M where I is his income, J is the number of jeans he sells, T is the number of T-shirts he sells, S is the number of shorts he sells, H is the number of hats he sells, and M is the number of meals he buys. If Edward makes $197 in a week and sells 5 pairs of jeans, 5 T-shirts, and 3 hats, and buys 3 of his meals, how many pairs of shorts did he sell?

In this problem, learn how to solve for the number of shorts sold by Edward using the equation I = 100 + 12J + 5T + 7S + 5H - 8M. Given his income of $197, and details about the number of jeans, T-shirts, hats sold, and meals bought, find the missing variable S (shorts). Perfect for students in grades 9-11 learning linear equations.

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