An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
For the first question, the equations representing the production costs are 100 x + 80 y = 32000 and 80 x + 64 y = 25600 , so the answer is (a).
For the second question, solving the system of equations p + q = 5 and p − q = 2 gives p = 3.5 and q = 1.5 , so the answer is (b).
Therefore, the final answers are (a) and (b).
The solutions are \boxed{(a), (b)}.
Explanation
Problem Analysis Let's analyze the given problem. We have two independent questions to solve.
Analyzing the first question (i) We are given the cost of production per unit for two products, A and B, as ₹ 100 and ₹ 80 respectively. The total production cost in a week is ₹ 32000. In the next week, the production cost reduces by 20%, and the total cost of producing the same number of units of each product is ₹ 25600. We need to find the equations that can be used to find the number of units of A, x , and the number of units of B, y .
Finding the equations The first equation can be formed as: 100 x + 80 y = 32000 In the next week, the production cost reduces by 20%. So, the new cost per unit for A is: 100 − 0.20 × 100 = 80 And the new cost per unit for B is: 80 − 0.20 × 80 = 64 So, the second equation can be formed as: 80 x + 64 y = 25600 Therefore, the correct option is (a).
Analyzing the second question (ii) We are given two equations: p + q = 5 p − q = 2 We need to find the values of p and q .
Solving the equations Adding the two equations, we get: ( p + q ) + ( p − q ) = 5 + 2 2 p = 7 p = 3.5 Substituting p = 3.5 into the first equation, we get: 3.5 + q = 5 q = 5 − 3.5 q = 1.5 Therefore, the correct option is (b).
Final Answer The correct options are: (i) (a) 100 x + 80 y = 32000 and 80 x + 64 y = 25600 (ii) (b) p = 3.5 , q = 1.5
Examples
Imagine you're running a small business that produces two types of goods. This problem helps you determine the number of each good you produced based on the total production costs. By setting up and solving a system of equations, you can efficiently manage your inventory and production planning. This method is also useful in budgeting and financial forecasting, ensuring that you can accurately predict costs and allocate resources effectively.
The device delivers a charge of 450 C over 30 seconds with a current of 15.0 A , resulting in approximately 2.81 × 1 0 21 electrons flowing through it. This is calculated using the relationship between current, charge, and the elementary charge of an electron.
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