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.

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Presentation transcript:

Algebra 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 = x + 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, x Y = 24, x 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