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.

Answer 1

To write the system of equations, we can define variables for the number of calculators and calendars ordered. We can then use the substitution method to solve the equations and determine the number of calculators and calendars ordered.

Step-by-step explanation:

To write the system of equations, we need to define some variables:

Let x be the number of calculators ordered

Let y be the number of calendars ordered

Based on the given information, we can create the following equations:

x + y = 80 (equation 1)

10x + 15y = 1000 (equation 2)

Using the substitution method, we can solve the system of equations by solving equation 1 for x:

x = 80 - y

Substituting this expression for x into equation 2:

10(80 - y) + 15y = 1000

800 - 10y + 15y = 1000

5y = 200

y = 40

Substituting this value of y into equation 1 to solve for x:

x + 40 = 80

x = 40

Therefore, 40 calculators and 40 calendars were ordered.