SOLUTION: Suppose Erika makes at least four times as much as Gabe does, and at most, half of what John makes. Let e, g, and j be the salaries of Erika, Gabe, and John respectively. Which of

Question 304937: Suppose Erika makes at least four times as much as Gabe does, and at most, half of what John makes. Let e, g, and j be the salaries of Erika, Gabe, and John respectively. Which of the following inequalities describe this situation?

A. e 4g and e j / 2
B. 4e g and e / 2 j
C. e > 4g and e < j / 2
D. 4e > g and e / 2 < j

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Your answer should be:

4g <= e <= j/2

You start with e >= 4g which means that erika makes at least 4 times as much as gabe.

If she makes at least 4 times as much as gabe, that means that she could make exactly 4 times as much as gabe, or more than 4 times as much as gabe.

e >= 4g is the same as 4g <= e.

You just read it backwards.

Algebraically, you would determine it as follows:

You start with:

e >= 4g

You subtract e from both sides of the equation and you subtract 4g from both sides of the equation to get:

-4g >= -e

You multiply both sides of the equation by -1 to get:

4g <= e

Multiplying both sides of the equation by -1 reverses the inequality which is why it resulted in 4g <= e.

The second part of your equation is:

e <= j/2

This means that erika makes less than or equal to 1/2 john's salary.

1/2 john's salary is the same as j/2.

Less than or equal is the same as at most.

She could make exactly as much as j/2, or she can make less than that.

Put these 2 pieces together and you get:

4g <= e <= j/2

I do not understand your selections.

The closest one would be C which reads e > 4g and e < j/2.

What's missing is the equality part of that.

It should have read e >= 4g and e <= j/2

Your first two selections are missing equality and inequality signs so they are meaningless.

Check your selections again:

the correct selection will be either:

e >= 4g and e <= j/2

or:

4g <= e <= j/2

Best I can do.

Let me know if you found the correct selection.

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