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Solving Real-Life Word Problems with Variables on Both Sides of Equations

This lesson focuses on writing and solving equations with variables on both sides from realistic scenarios. Students will explore various word problems, such as comparing costs of telephone plans, health club memberships, airplane rentals, and candle heights. By engaging with practical examples, students will practice forming equations and applying algebraic techniques to find solutions. Through these exercises, learners will enhance their problem-solving skills and gain confidence in using equations to represent real-life situations.

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Solving Real-Life Word Problems with Variables on Both Sides of Equations

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  1. Warm Up Exercise… • -12h + 39 = -4h – 17 (2) (1/3)(24p-66) = 3p + 43 (3) -19.4 – 15d + 22d = 4.4 (4) 14c – 8c + 7u = 37

  2. 2-4 Word Problems including variables on Both sides SWBAT write and solve equations with variables on both sides of the equal sign from a given realistic situation.

  3. One telephone company charges $16.95 per month and $0.05 per minute for local calls. Another company charges $22.95 per month and $0.02 per minute for local calls. For what number of minutes of local calls per month is the cost of the plans the same?

  4. One health club charges a $44 sign up fee and $30 per month. Another health club charges a $99 sign up fee and $25 per month. For what number of months is the cost the same?

  5. You and a pilot friend decide to rent an airplane to do some sightseeing. One service charges $100 plus $80 per hour, while another charges $250 plus $70 per hour for the same airplane. At what number of hours is the cost the same?

  6. A 15 inch candle burns at a rate of 0.25 inches per hour. A 20 inch candle burns at a rate of 1.5 inches per hour. At what time will the two candles be the same height?

  7. The length of a rectangle is 6 inches more than its width. The perimeter of the rectangle is 24 inches. What is the length of the rectangle?

  8. Mrs. Silvers wants to hire a painter to paint her house. Painter’s Plus charges $2,200 plus $45 per hour. Davis & Sons charges $1,850 plus $65 per hour. How many hours will the painters need to work for the two costs to be the same?

  9. Ace Truck Rental charges $54 a day plus $0.09 per mile. Roni’s Truck Rental charges $38.00 a day plus $0.13 per mile. For how many miles will the cost of renting a truck for one day at Ace equal the cost at Roni’s?

  10. Container A has 400 mL of water and is being filled at a rate of 8 mL per minute. Container B has 800 mL of water and is being drained at a rate of 8 mL per minute. How many minutes will it take for the two containers to have the same amount of water?

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