Hi! This is my summer packet for math class, and I'm on the last page. I can't figure it out. It's for next year's Algebra II class.
"Suppose you, your uncle, and your little brother are purchasing passes to Cedar Point (amusement park). You pay x dollars for your adult pass and $28 less for your little brother's pass. Your uncle pays the senior citizen rate, which is $16 less than the adult pass. Two hours after the park opens, 4668 adult passes, 118 senior citizen passes, and 634 child passes are sold. The park's income for these two hours is $186,320."
I did Q1 already.
Q2: Write a verbal model for the income of te amusement park after the first 2 hours.
Q3: Assign labels to the parts of the verbal model.
Q4: Translate the verbal model into an algebraic model.
Optional, greatly appreciated if you can help me on these:
Q5: Determine the individual prices of an adult pass, a child pass, and a senior citizen pass. What was the total cost for you, your brother, and your uncle to enter the park?
Q6: Suppose there is a 20% discount on both senior citizen and children's passes. Determine the income for the park in the first two hours.
Thanks! My main problems lie within the first few. The last two I could figure out on my own, but any help is welcome. Thanks again! I really appreciate it! :)
"Suppose you, your uncle, and your little brother are purchasing passes to Cedar Point (amusement park). You pay x dollars for your adult pass and $28 less for your little brother's pass. Your uncle pays the senior citizen rate, which is $16 less than the adult pass. Two hours after the park opens, 4668 adult passes, 118 senior citizen passes, and 634 child passes are sold. The park's income for these two hours is $186,320."
I did Q1 already.
Q2: Write a verbal model for the income of te amusement park after the first 2 hours.
Q3: Assign labels to the parts of the verbal model.
Q4: Translate the verbal model into an algebraic model.
Optional, greatly appreciated if you can help me on these:
Q5: Determine the individual prices of an adult pass, a child pass, and a senior citizen pass. What was the total cost for you, your brother, and your uncle to enter the park?
Q6: Suppose there is a 20% discount on both senior citizen and children's passes. Determine the income for the park in the first two hours.
Thanks! My main problems lie within the first few. The last two I could figure out on my own, but any help is welcome. Thanks again! I really appreciate it! :)
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Verbal model:
The number of adult passes sold in the first two hours times the price for one adult pass plus
the number of senior passes sold in the first two hours times the price for one senior pass plus
the number of child passes sold in the first two hours times the price for one child pass equals the park’s income for the first 2 hours.
Labels for each part:
Let x = the price for one adult pass
Let x – 16 equal the price for one senior pass
Let x – 28 equal the price for one child pass
In the first two hours,
The number of adult passes was 4668
The number of senior passes was 118
The number of child passes was 634
The park’s income for the first two hours was $186,320
Algebraic model:
4668x + 118(x – 16) + 634(x – 28) = 186320
The number of adult passes sold in the first two hours times the price for one adult pass plus
the number of senior passes sold in the first two hours times the price for one senior pass plus
the number of child passes sold in the first two hours times the price for one child pass equals the park’s income for the first 2 hours.
Labels for each part:
Let x = the price for one adult pass
Let x – 16 equal the price for one senior pass
Let x – 28 equal the price for one child pass
In the first two hours,
The number of adult passes was 4668
The number of senior passes was 118
The number of child passes was 634
The park’s income for the first two hours was $186,320
Algebraic model:
4668x + 118(x – 16) + 634(x – 28) = 186320