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Edward works at a clothing store and earns on commission. His weekly income depends on the clothing he sells, and he receives a fixed amount regardless of his sales. He also has to pay for his meals during his shifts, which reduces his income.

Edward's income can be modeled by the following equation:

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

where:
- [tex]\( I \)[/tex] is his income,
- [tex]\( J \)[/tex] is the number of jeans he sells,
- [tex]\( T \)[/tex] is the number of T-shirts he sells,
- [tex]\( S \)[/tex] is the number of shorts he sells,
- [tex]\( H \)[/tex] is the number of hats he sells,
- [tex]\( M \)[/tex] is the number of meals he buys.

If Edward makes \$197 in a week and sells:
- 5 pairs of jeans,
- 5 T-shirts,
- 3 hats,
- and buys 3 meals,

How many pairs of shorts did he sell?

Answer:



Answer :

GinnyAnswer
To solve for the number of pairs of shorts Edward sold, we start by carefully substituting the given values into the income equation:

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

We know from the problem statement that:
- [tex]\( I = 197 \)[/tex] (total income)
- [tex]\( J = 5 \)[/tex] (pairs of jeans sold)
- [tex]\( T = 5 \)[/tex] (T-shirts sold)
- [tex]\( H = 3 \)[/tex] (hats sold)
- [tex]\( M = 3 \)[/tex] (meals bought)
- [tex]\( S \)[/tex] (pairs of shorts sold) is what we're solving for.

Substitute these values into the equation:

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

Next, perform the arithmetic for the known terms:

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

Simplify the equation step by step:

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

Combine the constants:

[tex]\[ 197 = 100 + 60 + 25 + 15 - 24 + 7S \][/tex]
[tex]\[ 197 = 176 + 7S \][/tex]

Now isolate [tex]\( S \)[/tex] by subtracting 176 from both sides of the equation:

[tex]\[ 197 - 176 = 7S \][/tex]
[tex]\[ 21 = 7S \][/tex]

Finally, solve for [tex]\( S \)[/tex] by dividing both sides by 7:

[tex]\[ S = \frac{21}{7} \][/tex]
[tex]\[ S = 3 \][/tex]

So, Edward sold [tex]\( \boxed{3} \)[/tex] pairs of shorts.

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