Question

CAN SOMEONE HELP ME WITH THESE MATH QUESTIONS

1.

Which inequality models this problem?



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?


A.
2w + 2 • (3w) > 112


B.
2w + 2 • (3w) ≤112


C.
2w + 2 • (3w) < 112


D.
2w + 2 • (3w) ≥112

2.

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?


A.
22.4 cm

B.
28 cm

C.
14 cm

D.
42 cm


3.

Which inequality models this problem?



Eduardo started a business selling sporting goods. He spent $7500 to obtain his merchandise, and it costs him $300 per week for general expenses. He earns $850 per week in sales. What is the minimum number of weeks it will take for Eduardo to make a profit?


A.
300w > 7500 + 850w


B.
850w > 7500 + 300w


C.
850w < 7500 + 300w


D.
850w ≥ 7500 + 300w

4.

Reiko started a business selling home medical supplies. She spent $5200 to obtain her merchandise, and it costs her $550 per week for general expenses. She earns $900 per week in sales. What is the minimum number of weeks it will take for Reiko to make a profit?


A.
15 weeks


B.
14 weeks


C.
13 weeks


D.
12 weeks

5.

Jenny is eight years older than twice her cousin Sue’s age. The sum of their ages is less than 32. What is the greatest age that Sue could be?


A.
7


B.
8

C.
9

D.
10

Answer 1

1 B
2 C
3 D
4 A
5 B

Those are your answers

Answer 2

1.

Let the length be = l

Let the width be = w

The length of a rectangle is three times its width. So,
`l=3w`

If the perimeter is at most 112 centimeters, means it should exceed 112 cm.

We can define these as :
`2l+2w \leq 112`

Substituting l = 3w

`2(3w)+2w \leq 112` (option B)

2.

We have to solve the above equation here.

`2(3w)+2w \leq 112`

=>
`6w+2w \leq112`

=>
`8w \leq112`

=>
`w \leq14`

So, width can be at most 14 cm. (option C)

3.

Eduardo spent $7500 to obtain his merchandise, and it costs him $300 per week for general expenses.

He earns $850 per week in sales.

Let the number of weeks needed be = w

So, the inequality here becomes:

`850w>7500+300w` (option B)

4.

Reiko spent $5200 to obtain her merchandise, and it costs her $550 per week for general expenses.

She earns $900 per week in sales.

Let the weeks be w

So, inequality here becomes;

`900w>5200+550w`

Solving this we get;

`900w-550w>5200`

`350w>5200`

`w>14.85`

So, the minimum number of weeks needed to get profit will be 15 weeks (option A)

5.

Let Jenny's age be J

Let Sue's age be S

Jenny is eight years older than twice her cousin Sue’s age.

So we get,
`J=8+2S` ....(1)

The sum of their ages is less than 32. We get
`J+S<32` ....(2)

Substituting J=8+2S in (2)

`8+2S+S<32`

`3S+8<32`

`3S<32-8`

`3S<24`

`S<8`

We get Sue's age =7 (option A)