Question

An office manager orders one calculator or one calendar for each of the office's 80 employees. Each calculator costs $10, and each calendar costs $15. The entire order totaled $1,000.

Part A: Write the system of equations that models this scenario. (5 points)

Part B: Use substitution method or elimination method to determine the number of calculators and calendars ordered. Show all necessary steps. (5 points)

Answer 1

The system of equations modeling the scenario is C + K = 80 and 10C + 15K = 1000. By using substitution method, we find that the office manager ordered 40 calculators and 40 calendars.

Step-by-step explanation:

Part A: System of Equations

Let's denote the number of calculators as C and the number of calendars as K. Based on the given information, we can establish the following system of equations:

1. C + K = 80 (since one calculator or calendar is ordered for each of the 80 employees)
2. 10C + 15K = 1000 (calculators cost $10 each and calendars cost $15 each, totaling $1000)

Part B: Solving the System

We will use the substitution method to solve this system. We can express C in terms of K from the first equation:

• C = 80 - K

Now we substitute this expression for C into the second equation:

• 10(80 - K) + 15K = 1000
• 800 - 10K + 15K = 1000
• 5K = 200 (consolidating like terms)
• K = 40 (dividing both sides by 5 to solve for K)

Next, we substitute K = 40 back into the expression for C:

• C = 80 - 40
• C = 40

Therefore, the office manager ordered 40 calculators and 40 calendars.