Question

An office manager orders one calculator or one calendar for each of the office's 60 employees. Each calculator costs $12, and each calendar costs $10. The entire order totaled $700. 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

50 calculators and 10 calendars.

Explanation:

Part A: Let x be the number of calculators and y be the number of calendars ordered. Then we have the following system of equations:

x + y = 60 (the total number of items ordered is 60)

12x + 10y = 700 (the total cost of the order is $700)

Part B: To solve this system by substitution, we can isolate x from the first equation and substitute it into the second equation. This gives us:

x = 60 - y

12(60 - y) + 10y = 700

Simplifying and solving for y, we get:

720 - 12y + 10y = 700

-2y = -20

y = 10

Therefore, the number of calendars ordered is 10. To find the number of calculators ordered, we can plug in y = 10 into the first equation and get:

x + 10 = 60

x = 50

Therefore, the number of calculators ordered is 50.