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.

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

Part A:

Let x represent the number of calculators ordered and y represent the number of calendars ordered.

The total cost equation is:
12x + 10y = 700

The total number of items equation is:
x + y = 60

Part B:

From equation 2, we can rewrite it as x = 60 - y and substitute into equation 1:

12(60 - y) + 10y = 700
720 - 12y + 10y = 700
-2y = -20
y = 10

Substitute y back into equation 2:

x + 10 = 60
x = 50

Therefore, 50 calculators and 10 calendars were ordered.