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Solving Problems with Equations

Solving Problems with Equations. Solving Problems with Equations. 1. Read the problem and look for the question. Use a variable to represent the unknown quantity. … How many people came to the concert?. Let p = the number of people who came to the concert. ... What was the monthly charge?.

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Solving Problems with Equations

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  1. Solving Problems with Equations

  2. Solving Problems with Equations 1. Read the problem and look for the question. Use a variable to represent the unknown quantity. …How many people came to the concert? Let p = the number of people who came to the concert. ...What was the monthly charge? Let m = the amount of the monthly charge.

  3. Solving Problems with Equations 2. Reread the problem and use the information to write an equation using the variable you named. The phone company charges a fixed rate of $25/month plus $0.20 per call. If the monthly charge was $30.40, how many calls were made? Let c = the number of calls. 0.2c + 25 = 30.40

  4. Solving Problems with Equations 3. Solve the equation. 0.2c + 25 = 30.40 0.2c = 5.40 c = 27 4. Answer the question. There were 27 calls made during the month in question.

  5. Solving Problems with Equations Othello drove himself and several friends to Freedom Weekend Aloft in his new van. The charge was $4.50 per person in the van and a $10.00 parking fee. If the total charge was $50.50, how many people were in the van?

  6. Find the question and name the variable. …How many people were in the van? Let p = the number of people in the van. Use the other information to write an equation. 4.50p + 10 = 50.50

  7. Solve the equation 4.50p + 10 = 50.50 - 10 - 10 4.50 p = 40.50 4.50 4.50 p = 9 Answer the question There were 9 people in the van.

  8. Solving Problems with Equations Dish Network charges $30 installation plus a monthly rate. If Malvolio paid $509.88 during the first year, what was the monthly charge? Find the question and name the variable. Let m = the monthly charge

  9. Use the other information to write an equation. 12m + 30 = 509.88 Solve the equation 12m = 479.88 m = 39.99 Answer the question The monthly charge is $39.99

  10. Solving Problems with Equations Ophelia works on commission plus a base salary selling cosmetics. She earns $250 per week plus 6% of her sales. One week she made $347.50. What was the amount of her sales?

  11. Find the question and name the variable. Let s = the amount of her sales. Write an equation. 0.06s + 250 = 347.50 Solve the equation 0.06s = 97.5 s = 1625 Answer the question She sold $1625 worth of cosmetics

  12. Solving Problems with Equations The drama club spent $850 on costumes and printing tickets for the play “Einstein meets Pythagoras.” If they charge $5.00 per ticket, how “Pyth” many tickets must they sell to make a profit of $500? “Al”

  13. Find the question and name the variable. Let t = the number of tickets Write an equation. 5t - 850 = 500 Solve the equation 5t = 1350 t = 270 Answer the question They must sell 270 tickets

  14. Solving Problems with Equations How many liters of water must be added to 50 liters of a 30% acid solution in order to produce a 20% acid solution? Find the question and name the variable. Let x = the number of liters of water added to create a 20% solution.

  15. Sometimes a chart is helpful in these kinds of problems. (# of liters)(% acid) = liters of acid Orig Solution 50 30 (50)(.30)=15 Water Added x 0 0 New Solution x + 50 20 0.2(x + 50) Write an equation. Since the number of liters of acid has not changed, the equation sets the liters of acid in the original solution equal to the liters of acid in the new solution. 0.2(x + 50) = 15

  16. Solve the equation 0.2(x + 50) = 15 0.2x + 10 = 15 0.2x = 5 x = 25 Answer the question To produce a 20% solution, add 25 liters of water.

  17. Desdemona opened her purse and found dimes, quarters, and nickels with total value of $1.90. There are twice as many dimes as $$$$ quarters and half as many nickels as quarters. How many coins of each type did Desdemona have in her purse?

  18. Name the variable(s) Let n = the number of nickels 2n = the number of quarters 4n = the number of dimes Write an equation Since a nickel is worth $.05, a quarter is worth $.25, and a dime is worth $.10, the equation is: .05n + .25(2n) + .10(4n) = 1.90

  19. Solve the equation .05n + .5n + .4n = 1.90 .95n = 1.90 n = 2 Answer the question Since n = 2, there are 2 nickels Since 2n = 4, there are 4 quarters Since 4n = 8, there are 8 dimes

  20. Your Turn! Homework Worksheet (1 - 11)

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