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Alfred wants to waste less than 175 gallons of water this week. Every day that he waters the lawn, he wastes 59 gallons of water. Every day that he washes his car, he wastes 28 gallons of water.
Write an inequality that represents the number of days Alfred should water the lawn
(L) and wash his car
(C) to achieve his goal.

Alfred wants to waste less than $175$ gallons of water this week. Every day that he waters the lawn, he wastes $59$ gallons of water. Every day that he washes his car, he wastes $28$ gallons of water. $\newline$ Write an inequality that represents the number of days Alfred should water the lawn $\newline$ (L) and wash his car $\newline$ (C) to achieve his goal.

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Modeling with linear inequalities

Full solution

Q. Alfred wants to waste less than

175

gallons of water this week. Every day that he waters the lawn, he wastes

59

gallons of water. Every day that he washes his car, he wastes

28

gallons of water.

\newline

Write an inequality that represents the number of days Alfred should water the lawn

\newline

(L) and wash his car

\newline

(C) to achieve his goal.

Define Variables: Let's define the variables: $\newline$ $L =$ number of days Alfred waters the lawn $\newline$ $C =$ number of days Alfred washes his car $\newline$ We are given that watering the lawn wastes $59$ gallons of water per day and washing the car wastes $28$ gallons of water per day. Alfred's goal is to waste less than $175$ gallons of water in total.
Write Inequality: We can write an inequality to represent the total amount of water wasted by both activities: $\newline$ $59L + 28C < 175$ $\newline$ This inequality states that the total gallons of water wasted from watering the lawn for $L$ days and washing the car for $C$ days should be less than $175$ gallons.
Check Units: To check for any math errors, we can consider the units involved. The left side of the inequality represents gallons of water ( $59$ gallons per lawn-watering day times the number of lawn-watering days, plus $28$ gallons per car-washing day times the number of car-washing days), and the right side represents gallons of water ( $175$ gallons). Since the units match, there is no math error in the inequality.

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