Transcript 7.4 Application of Linear Systems

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