An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Define variables: Let c be the number of cold beverages and h be the number of hot beverages.
Write the equation for total receipts: 1.5 c + 2 h = 360 .
Write the equation for the relationship between cold and hot beverages: c = 4 h .
The system of equations is: c = 4 h and 1.5 c + 2 h = 360 , which represents the beverage sales on Saturday. c = 4 h 1.5 c + 2 h = 360
Explanation
Setting up the equations Let c be the number of cold beverages sold and h be the number of hot beverages sold. The problem states that cold beverages cost $1.50 and hot beverages cost $2.00 . The total receipts on Saturday were $360 . This can be represented by the equation 1.50 c + 2.00 h = 360 . The problem also states that 4 times as many cold beverages were sold as hot beverages, which can be represented by the equation c = 4 h . Therefore, the system of linear equations that represents the beverage sales on Saturday is:
c = 4 h 1.5 c + 2 h = 360
Identifying the correct system of equations The system of linear equations that represents the beverage sales on Saturday is:
c = 4 h 1.5 c + 2 h = 360
This corresponds to the second option.
Examples
Understanding systems of equations can help in managing inventory and sales in a store. For example, if a store sells two products with different costs and profit margins, and the store manager wants to achieve a specific total revenue while selling a certain ratio of the two products, they can set up a system of equations to determine the number of each product to sell. This ensures that the revenue target is met while maintaining the desired sales ratio, optimizing the store's profitability and inventory management.
The total charge delivered by a current of 15.0 A over 30 seconds is 450 Coulombs. This charge corresponds to approximately 2.81 x 10^21 electrons. Thus, around 2.81 x 10^21 electrons flow through the device during that time.
;
