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Axel and Carl both volunteer at a science museum. The manager needs one helper at a time for at most 18 hours this month. Axel wants to work at least 6 hours. The manager wants Carl to work no more than twice as many hours as Axel. Let a represent the number of hours that Axel works. Let c represent the number of hours Carl works. Which system of inequalities represents the constraints of this problem situation?

Respuesta :

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We want to find a system of inequalities that models the given situation.

We will find the system:

a + c ≤ 18

a ≥ 6

c ≤ 2*a

First we define the variables:

  • c = number of hours that Carl works.
  • a = number of hours that Axel works

The given information is:

The manager needs one helper at a time for at most 18 hours.

From this we can write:

a + c ≤ 18

Axel wants to work at least 6 hours.

a ≥ 6

The manager wants carl to work no more than twice as many hours as Axel.

c ≤ 2*a

The system is then:

a + c ≤ 18

a ≥ 6

c ≤ 2*a

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