Question

Two companies have made Evelyn job offers. B-Innovative, Inc., provides a one-time signing bonus of $4,100 and pays $1,095 a week. Tech-O-Matic provides a one-time signing bonus of $2,300 and pays $1,284 a week. Write an inequality to determine the number of weeks w () Evelyn must work so that the income earned at Tech-O-Matic is greater than or equal to the income earned at B-Innovative, Inc.

a. Write the question or problem statement for the situation.
_______________________________________
b. Write the phrase that represents the inequality symbol in the problem and the corresponding inequality symbol.
_______________________________________
c.Write the general form of the inequality. _______________________________________________________________________________
d.Write the verbal and variable expression for the left side of the inequality. _______________________________________________________________________________
e.Write the verbal and variable expression for the right side of the inequality. _______________________________________________________________________________
f. Write the final algebraic inequality with variables on both sides. Include what the variable represents in the problem. Include appropriate units. _______________________________________________________________________________

Answer 1

Evelyn must work for at least approximately 9.5238 weeks (or 9.524 weeks, rounding up) at Tech-O-Matic for her income there to be greater than or equal to her income at B-Innovative.

Explanation:

To determine the number of weeks (w) that Evelyn must work so that the income earned at Tech-O-Matic is greater than or equal to the income earned at B-Innovative, Inc., you can set up the following inequality:

Income at Tech-O-Matic (I_Tech-O-Matic) ≥ Income at B-Innovative (I_B-Innovative)

The income at Tech-O-Matic consists of the signing bonus plus the weekly pay:

I_Tech-O-Matic = $2,300 + $1,284w

The income at B-Innovative consists of the signing bonus plus the weekly pay:

I_B-Innovative = $4,100 + $1,095w

Now, set up the inequality:

$2,300 + $1,284w ≥ $4,100 + $1,095w

To solve for w, you'll want to isolate the variable on one side of the inequality. Start by moving all the terms involving w to one side:

$1,284w - $1,095w ≥ $4,100 - $2,300

Now, simplify:

$189w ≥ $1,800

To solve for w, divide both sides of the inequality by 189:

w ≥ $1,800 / $189

w ≥ 9.5238 (rounded to four decimal places)

So the answer is 9.5238

Explanation: