Math

QuestionLet xx be hours worked in housecleaning and yy in sales. Write the inequalities: x+y41x + y \leq 41 and 5x+8y2545x + 8y \geq 254.

Studdy Solution

STEP 1

Assumptions1. The total working hours per week cannot exceed41 hours. . The housecleaning job pays 5perhour.<br/>3.Thesalesjobpays5 per hour.<br />3. The sales job pays 8 per hour.
4. The total earnings per week must be at least $254.

STEP 2

Let's denote the number of hours worked at the housecleaning job as hh and the number of hours worked at the sales job as ss.

STEP 3

The first condition is that the total number of hours worked at both jobs cannot exceed41 hours. We can write this as an inequalityh+s41h + s \leq41

STEP 4

The second condition is that the total earnings from both jobs must be at least 254.Theearningsfromthehousecleaningjobare254. The earnings from the housecleaning job are handtheearningsfromthesalesjobare and the earnings from the sales job are 8s.Wecanwritethisasaninequality. We can write this as an inequalityh+8s254h +8s \geq254$

STEP 5

The final condition is that the number of hours worked at each job must be non-negative, as it's not possible to work a negative number of hours. We can write this as two inequalitiesh0h \geq0s0s \geq0

STEP 6

So, the system of inequalities that shows the various numbers of hours you can work at each job ish+s41h + s \leq415h+8s2545h +8s \geq254h0h \geq0s0s \geq0This system of inequalities represents all possible combinations of hours you can work at each job to meet your requirements.

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