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Brett wants to paint his master bedroom. The paint costs $21 per gallon and the primer costs $15 per gallon. He does not want to exceed $185 for the paint and primer. He has determined that he needs at least 5 gallons of paint and primer in total. If p represents the number of gallons of paint and r represents the number of gallons of primer, which system of inequalities represents Brett’s situation?

Respuesta :

Answer:

[tex]21p + 15r \leq 185[/tex]

[tex]p + r \geq 5[/tex]

Explanation:

Two inequalities can be derived from the question.

1. Total Cost Inequality

If paint (p) costs $21 per gallon, primer (r) costs $15 per gallon, and Brett does not want to exceed $185, we can represent this by the inequality below.

[tex]21p + 15r \leq 185[/tex].

This means total cost of paint and primer will be less than or equal to $185.

2. Total Quantity Inequality

Brett determined that he needs at least 5 gallons in total, and we represent this by the inequality below.

[tex]p + r \geq 5[/tex]

This means total quantity of paint and primer must be greater than 5.

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