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
Let x be the number of calculators ordered and y be the number of calendars ordered.
Then, we have:
x + y = 60 (since one calculator or calendar is ordered for each employee)
12x + 10y = 700 (the total cost of the order is $700, where each calculator costs $12 and each calendar costs $10)
Part B: Solve the system of equations using any method.
We can solve this system by substitution or elimination. Let's use elimination:
Multiplying the first equation by 10, we get:
10x + 10y = 600
Subtracting this equation from the second one, we get:
2x = 100
Solving for x, we get:
x = 50
Substituting x = 50 into the first equation, we get:
50 + y = 60
Solving for y, we get:
y = 10
Therefore, the office manager ordered 50 calculators and 10 calendars.
Let's use the variables c and d to represent the number of calculators and calendars, respectively.
The first equation represents the total number of items ordered:
c + d = 60
The second equation represents the total cost of the order:
12c + 10d = 700
Therefore, the system of equations is:
c + d = 60
12c + 10d = 700