the cost of operating a day school for a day is partly constant and partly varies as the number of students a. it costs sh.40000 to run when there are 500 students and sh.64000 when there are 900 students. form an equation for the cost c and number of students n?. (b). what would be the cost of running the school when there are 700 students. (c). if the cost of running the school is sh.82000 per day, how many students are in the school?
c = a + b n
40,000 = a + 500 b
64,000 = a + 900 b
---------------------------- subtract
-24,000 = -400 b
b = 60
40,000 = a + 500* 60 = a + 30,000
a = 10,000
so
c = 10,000 + 60 n
I think you can take it from there.
I don't know
anonymous first try to do it please
c = 10,000 + 60 n
If n is 700 students then
c = 10,000 + 60*700
If the cost is 82000
then
82,000 + 10,000 + 60 n
60 n = 72,000
n = 7,200 / 6 = 1200
To form an equation for the cost "c" and the number of students "n," we need to understand the relationship between the cost and the number of students. According to the problem, the cost is partly constant and partly varies as the number of students.
Let's break this down into two components:
1. The constant part: This is the cost of operating the school regardless of the number of students. Let's denote it as "a."
2. The variable part: This is the additional cost that depends on the number of students. Let's denote it as "bn," where "b" is the cost per student.
Based on the information given, we can create two equations using the given costs at different student levels:
Equation 1: 40,000 = a + 500b
Equation 2: 64,000 = a + 900b
Now we have two equations with two unknowns (a and b). We can solve this system of equations to find their values.
Subtracting Equation 1 from Equation 2 eliminates "a":
24,000 = 400b
b = 60
Substituting the value of "b" back into either equation:
40,000 = a + 500 * 60
40,000 = a + 30,000
a = 40,000 - 30,000
a = 10,000
Therefore, the equation for the cost "c" in terms of the number of students "n" is:
c = 10,000 + 60n
Now let's answer the other parts of the question:
(b) To find the cost of running the school when there are 700 students:
c = 10,000 + 60 * 700
c = 10,000 + 42,000
c = 52,000 shillings
The cost of running the school with 700 students would be 52,000 shillings.
(c) If the cost of running the school is 82,000 shillings per day, we can set up the equation and solve for the number of students "n":
82,000 = 10,000 + 60n
72,000 = 60n
n = 1,200
Therefore, there are 1,200 students in the school if the cost of running it is 82,000 shillings per day.