Question

Greg owns a clothing store where he designs pairs of shorts, s, and T-shirts, t.

He sells the shorts for $12 and the T-shirts for $5 each. Greg can work 15
hours a day, at most. It takes him 30 minutes to design a T-shirt and an hour
and 30 minutes to design a pair of shorts. He must design at least 10 items
each day, but he cannot design more than 25 items in one day. Which set of
inequalities below represents this scenario?
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A. S2 10 - t, s s 25 - t, ss 10 -0.33t, s 2 0; t2 0
B. S 2 10+ t, s s 25+ t, ss 10-0.33t, s 2 0;t0
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c. ss 10 - t, s2 25- t, ss 10 -0.33t, s 2 0; t2 0
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D. S 2 10 - tss 25-ts 10 -0.33t; s 2 0;t2 0

Answer 1

s ≥ 10 - t, s ≤ 25 - t, s ≤ 10 -0.33t, s ≥ 0; t ≥ 0

Answer 2

The answer choices are garbled, thus you cannot pick among them. Below, you can see how to determine this system:

• 0.33t + s ≤ 10

• t + s ≥ 10

• t + s ≤ 25

• t ≥ 0

• s ≥ 0

Step-by-step explanation:

1. Name your variables:

• Number of shorts: s

• Number of T-shirts: t

2. He sells the shorts for $12

Then, the value of s shorts is represented by:

• 12s

3. He sells the T-shirts for $5 each.

Then, the value of t Tshirts is:

• 5t

4. Total value = value of shorts + value of T-shirts:

• Value of sales = 12s + 5t

5. It takes him 30 minutes to design a T-shirt.

Then, using 30 minutes = 0.5 hours, the time to design t Tshirts is:

• 0.5t

6. It takes him an hour and 30 minutes to desing a pair of shorts

Then, using an hour and 30 minutes = 1.5 hours, the time to desing s pairs of shorts is:

• 1.5s

7. Greg can work 15 hours a day, at most.

Then, the total time must be equal or less than 15 hours:

• 0.5t + 1.5s ≤ 15 ↔ first inequality

8. He must design at least 10 items each day,

Then, the total number of items is equal to or greater than 10:

• t + s ≥ 10 ↔ second inequality

9. He cannot design more than 25 items in one day.

Then, the total number of items is equal to or less than 25:

• t + s ≤ 25 ↔ third inequality

10. You must add the natural constraints: the items cannot be negative:

• t ≥ 0

• s ≥ 0

Summarizing the inequalities are:

• 0.5t + 1.5s ≤ 15

• t + s ≥ 10

• t + s ≤ 25

• t ≥ 0

• s ≥ 0

Divide the first inequality by 1.5:

• 0.33t + s ≤ 10

And the five inequalities can be written as:

• 0.33t + s ≤ 10

• t + s ≥ 10

• t + s ≤ 25

• t ≥ 0

• s ≥ 0