Describe the key attributes of is function.
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We are given a problem that can be solved using a system of linear equations. Let A, be the number of adults, and S the number of students. Since there are in total 142 people and there were two days, this means that the sum of the number of adults and the number of students must be 284, which can be written mathematically as follows:
This is our first equation. The second equation is found using the total sales of $1948. Since the ticket per adult is $8 and per student is $5, we have the following equations:
To solve this equation we will solve for A in equation (1), by subtracting S to both sides;
Now we will replace this value in equation (2):
Now we will apply the distributive property:
Addins like terms:
Subtracting 2272 to both sides;
Dividing both sides by -3:
Now we replace this value in equation (1), where we have already solved for A:
Therefore, there were sold 108 student tickets and 140 adult tickets.
Answer:
Step-by-step explanation:
<u>Function modeling</u>
Real-life situations often require the help of mathematics to model numerically what happens when the variables involved can change. It could even be used to predict some expected outcomes from those models.
The problem states Janice receives $.40 per pound when he recycles less or equal than 99 pounds of aluminum. If x is the number of recycled pounds, then the amount of money he receives is
We also know that if he recycles more than 100 pounds of aluminum, the pay increases to $0.5 per pound. In that case, the amount of money is
This is a case where the function is defined differently depending on the conditions of the input variable x. It's called a piecewise function. The function can be written as
Note the function is not well constructed because there is a gap for x=100 where M is not defined. If we establish that for 100 pounds the payment is $0.5, then the second piece would include x=100