Question

Help with math please!?

The length of a rectangle is three times its width. If the perimeter is at most 112 centimeters, what is the greatest possible value for the width? Write an inequality to model the problem.

A. 2w + 2 ? (3w) ≥112

B. 2w + 2 ? (3w) < 112

C. 2w + 2 ? (3w) > 112

D. 2w + 2 ? (3w) ≤112

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The length of a rectangle is three times its width. If the perimeter is at most 112 centimeters, what is the greatest possible value for the width? Solve the problem.

A. 42 cm

B. 22.4 cm

C. 14 cm

D. 28 cm

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Josephine started a business selling cosmetics. She spent $4500 to obtain her merchandise, and it costs her $200 per week for general expenses. She earned $550 per week in sales. What is the minimum number of weeks it will take for Josephine to make a profit? Write an inequality to model the problem.

A. 550w > 4500 + 200w

B. 200w > 4500 + 550w

C. 550w < 4500 + 200w

D. 200w ≥ 4500 + 550w

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Josephine started a business selling cosmetics. She spent $4500 to obtain her merchandise, and it costs her $200 per week for general expenses. She earned $550 per week in sales. What is the minimum number of weeks it will take for Josephine to make a profit? Solve the problem.

A. 12 weeks

B. 13 weeks

C. 14 weeks

D. 15 weeks

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Mia is three years older than twice her sister Brooke's age. The sum of their ages is less than 30. What is the greatest age Brooke could be?

A. 7

B. 8

C. 9

D. 10

Thanks answer please

Answers

1)

Ans) D. 2w + 2 ? (3w) ≤ 112

Note that they said at most 112. Thus, 112 is included as well.

This means the inequality is less than or equal to, not just less than.

2)

The greatest value of the perimeter is 112.

Thus, we have: 2w + 2 ? (3w) = 112

Solving, we will get:

2w + 6w = 112

8w = 112

w = 14 cm

Ans) C. 14 cm

3)

Ans) A. 550w > 4500 + 200w

550w is the amount earned in w weeks.

4500 + 200w is the amount she used in w weeks.

Thus, when 550w > 4500 + 200w, it means she will have earned more than she spent.

4)

We will solve question 3)'s inequality

550w > 4500 + 200w

550w - 200w > 4500

350w > 4500

w > 12.857 weeks

Since we are asked the minimum amount of weeks, we will need to round this up to 13 weeks.

Ans) B. 13 weeks

5)

Let Brooke be x years old

Mia is 2x + 3 years old

Their total age is x + (2x + 3) = 3x + 3

Their age is less than 30, so we have:

3x + 3 < 30

3x < 27

x < 9

Here is the tricky part. Their total age is less than 30, so 30 is not included.

This means that Brooke's age cannot be 9, and must be strictly less than 9.

Thus, her greatest possible age will have to be 9 - 1 = 8

Ans) B. 8

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