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-Dominant- [34]
3 years ago
8

 As a salesperson, you are paid $92 per week plus $4 per sale. This week you want your pay to be at least $200. Write an inequal

ity for the number of sales you need to make, and describe the solutions.
A)92 - 4s ≤ 200; s ≤ 26
B)92 + 4s ≥ 200; s ≥ 26
C)92 - 4s ≤ 200; s ≤ 27
D)92 + 4s ≥ 200; s ≥ 27
Mathematics
1 answer:
KatRina [158]3 years ago
8 0
The equation has to include the total pay that is greater than (≥) $200 AND the $4 per sale has to be added to the $92 weekly rate. The only option that is valid then is D) 92 +4s ≥ 200.

Let's solve for s:

92 + 4s ≥ 200
subtract 92 from both sides

4s ≥ 108
divide both sides by 4

s ≥ 27


ANSWER: D) 92 + 4s ≥ 200; s ≥ 27

Hope this helps! :)
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<h3>Answer:   16 ft by 25 ft</h3>

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Explanation:

Refer to the diagram below.

The outer dimensions 24 ft and 33 ft shrink down to 24-2x ft and 33-2x ft respectively. This subtraction of 2x is due to subtracting two copies of x per side.

The carpet has area of (24-2x)(33-2x)

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So we set 400 equal to that previous expression and solve for x

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792-48x - 66x + 4x^2 = 400

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4x^2 - 114x + 792-400 = 0

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From here, use the quadratic formula to isolate x.

Plug in a = 4, b = -114, c = 392

x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-114)\pm\sqrt{(-114)^2-4(4)(392)}}{2(4)}\\\\x = \frac{114\pm\sqrt{6724}}{8}\\\\x = \frac{114\pm82}{8}\\\\x = \frac{114+82}{8} \ \text{ or } \ x = \frac{114-82}{8}\\\\x = \frac{196}{8} \ \text{ or } \ x = \frac{32}{8}\\\\x = 24.5 \ \text{ or } \ x = 4\\\\

The two possible solutions are x = 24.5 and x = 4

But if x = 24.5, then 24 - 2x = 24 - 2*24.5 = -25 which isn't possible. We cannot have a negative width or negative length for the carpet.

Luckily x = 4 does work since

24 - 2x = 24 - 2*4 = 16

33 - 2x = 33 - 2*4 = 25

Both results are positive.

Therefore, the carpet has dimensions of <u>16 ft by 25 ft</u>

Check: 16*25 = 400, so the answer is confirmed

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hope this helps
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