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 step

Answer 1

Part A:

Let x be the number of calculators ordered.
Let y be the number of calendars ordered.

The system of equations is:

x + y = 60 (one calculator or one calendar for each employee)
12x + 10y = 700 (total cost of the order)

Part B:

Using the substitution method:

x + y = 60 --> x = 60 - y
12x + 10y = 700

Substituting x with 60 - y:

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

Substituting y with 10:

x + 10 = 60
x = 50

Therefore, 50 calculators and 10 calendars were ordered.

Answer 2

Part A:

Let's assume 'x' represents the number of calculators and 'y' represents the number of calendars ordered.

The first equation can be formed based on the number of employees:
x + y = 60

The second equation can be formed based on the total cost of the order:
12x + 10y = 700

Part B:

To solve the system of equations, we will use the elimination method.

x + y = 60 ---(1)
12x + 10y = 700 ---(2)

To eliminate one of the variables, let's multiply equation (1) by 10:

10x + 10y = 600 ---(3)

Now we can subtract equation (3) from equation (2) to eliminate 'y':

(12x + 10y) - (10x + 10y) = 700 - 600
2x = 100
x = 50

Substituting the value of x back into equation (1), we can solve for 'y':

50 + y = 60
y = 60 - 50
y = 10

Therefore, the office manager ordered 50 calculators and 10 calendars.

Answer 3

Part A:

Let's define two variables to represent the number of calculators and calendars ordered.

Let x be the number of calculators ordered.
Let y be the number of calendars ordered.

According to the given information, the office manager orders one calculator or one calendar for each of the 60 employees. So we can write the first equation as:

x + y = 60

Each calculator costs $12, and each calendar costs $10. The entire order totaled $700. Since the office manager buys 60 items in total, we can write the second equation as:

12x + 10y = 700

So, the system of equations that models this scenario is:
Equation 1: x + y = 60
Equation 2: 12x + 10y = 700

Part B:
To find the number of calculators and calendars ordered, we can solve this system of equations using either the substitution or elimination method. Let's use the elimination method.

Multiply Equation 1 by 10 to get rid of the coefficients of y:
10(x + y) = 10(60)
10x + 10y = 600

Now we have two equations:
10x + 10y = 600
12x + 10y = 700

Subtract the first equation from the second equation to eliminate y:
(12x + 10y) - (10x + 10y) = 700 - 600
2x = 100
x = 50

Substitute the value of x into Equation 1 to find y:
50 + y = 60
y = 60 - 50
y = 10

Therefore, the office manager ordered 50 calculators and 10 calendars.