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Trenton works for a company that is promoting its line of LED lightbulbs. He is selling boxes of the lightbulbs at a local store. A box of 60-watt bulbs costs $7.00, and a box of 100-watt bulbs costs $12.00. During the promotion, Trenton wants to sell more than 100 boxes total and make at least $1,000. The graph and the system of inequalities represent this situation, where x represents the number of boxes of 60-watt bulbs sold and y represents the number of boxes of 100-watt bulbs sold. 7x + 12y ≥ 1,000 x + y > 100 Which solution is valid within the context of the situation?
A. (90,25)
B. (40,64.50)
C. (30,80)
D. (200,-10)

Respuesta :

Answer:

C) 30,80 PLATO

Step-by-step explanation:

This is the only answer that goes into the solution set on the graph, and the rest can be ruled out because they have either a half (you can't have half a bulb lol) or negative (how you gone have negative bulbs smh) and if you didn't rule out all others with these two they also have to LOOk like they are in the solution set. Thats how i solve ALL of them and get them correct.

Hopefully i helped and corrected the wrong answer up there!

shristiparmar1221

This question is based on system of linear equation.Therefore, the correct option is ( C ), (30,80)  solution is valid within the context of the situation.

Given:

7x + 12y ≥ 1,000

x + y > 100

We need to determined the solution which  is valid within the context of the situation.

According to question,

A. (90,25)

Put this value in given both equation.

We get,

  • 7(90) + 12(25) ≥ 1,000  

        630 + 300 [tex]\ngeqslant[/tex] 1000

   ⇒ 930 [tex]\ngeqslant[/tex] 1,000

  • x + y > 100

       90 + 25 > 100

   ⇒ 115 > 100

B. (40,64.50)

  • 7(40) + 12(64.50) ≥ 1,000  

        280 + 774 [tex]\geq[/tex] 1000

   ⇒  1054 [tex]\geq[/tex] 1000

  • x + y > 100

       40 + 64.50 >100

   ⇒ 104.50 > 100

C. (30,80)

  • 7(30) + 12(80) ≥ 1,000

        210 + 960 [tex]\geq[/tex] 1000

   ⇒  1170 [tex]\geq[/tex] 1000

  • x + y > 100

        30 + 80 = 110 >100

D. (200,-10)

  • 7(200) + 12(-10) ≥ 1,000

       1400 -120 [tex]\geq[/tex] 1000

   ⇒ 1280 [tex]\geq[/tex]1000

  • x + y > 100

       200 - 10 >100

  ⇒  190>100

Therefore, the correct option is (C), (30,80)  solution is valid within the context of the situation.because this is the only answer that goes into the solution set on the graph, and the rest can be ruled out because they have either a half (you can't have half a bulb lol) or negative (how you gone have negative bulbs smh).

For more details, prefer this link:

https://brainly.com/question/11897796