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Algebra 1 7.4 Applications of Linear Systems Amusement Park • Two families go to Busch Gardens. • In Family A, they buy 3 children (ages 3 to 9) tickets and 2 adult (10 and up) tickets. • For family B, they buy 4 children (ages 3 to 9) and 5 adult (10 and up) tickets. • Family A’s total was $290 • Family B’s total was $536 • What is the price for a child’s ticket? Think A System of Linear Equations • In Family A, they buy 3 children (ages 3 to 9) tickets and 2 adult (10 and up) tickets. • For family B, they buy 4 children (ages 3 to 9) and 5 adult (10 and up) tickets. • Family A’s total was $290 • Family B’s total was $536 • What is the price for a child’s ticket? Let x = $ of children’s tickets Let y = $ of adult tickets • In Family A, they buy 3 children (ages 3 to 9) tickets and 2 adult (10 and up) tickets. • For family B, they buy 4 children (ages 3 to 9) and 5 adult (10 and up) tickets. • Family A’s total was $290 • Family B’s total was $536 • What is the price for a child’s ticket? Think A System of Linear Equations • In Family A, they buy 3 children (ages 3 to 9) tickets and 2 adult (10 and up) tickets. • Family A’s total was $290 • Equation for Family A 3x + 2y = 290 How about the equation for Family B? Equation for Family B • For family B, they buy 4 children (ages 3 to 9) and 5 adult (10 and up) tickets. • Family B’s total was $536 • Equation for Family B 4x + 5y = 536 Now you have the system 3x + 2y = 290 4x + 5y = 536 Solve it by the method of your choice. Answer x = 54 So the question asked for the price of a child’s ticket which would be $54. Example #2 Bake Sale • You purchased 12 pounds of sugar and 15 pounds of flour. Your total cost was $9.30 The next day, at the same prices, you purchased 4 pounds of sugar and 10 pounds of flour. Your total cost the second day was $4.60 Find the cost per pound of the sugar and the flour purchases. Bake Sale • Let x = cost of sugar per pound • Let y = cost of flour per pound • • • • 12x + 15 y = 9.30 4x + 10 y = 4.60 Now Solve It by the Method of Your Choice! X = .40 and y = .30 So the price of sugar is .40 per pound and the price of flour is .30 per pound Example #3 • You are offered two different sales jobs. • Job A offers an annual salary of $30,000 plus a year-end bonus of 1% of your total sales. • Job B offers an annual salary of $24,000 plus a year-end bonus of 2% of your total sales. • How much would you have to sell to earn the same amount in each job? Set up the system • Y = 30,000 + .01x • Y = 24,000 +.02x • And Solve • X = 600,000 and y = 36,000 • You would have to sell $600,00 worth of merchandise to earn the same amount of money in each job. Homework • P. 422 #46-50 • P. 238 #23-25 look back over your notes on 4.5 Direct Variation