The total expenditure of a household is partly constant and partly varies directly as a size of household find the equation connecting d and s if when Q=300 and when d=400 and s=6
what are d and s, and where does Q come in?
I guess s is the size, but what is the expenditure?
It seems you want an equation like
expenditure = const + variable * size
That is, something like y = b+mx, but with the names changed as needed.
You will need two data points to determine the constant and the variable
To find the equation connecting the total expenditure (Q), the constant expenditure (k), and the variable expenditure (ds), we need to establish the relationship between Q and s.
We know that the total expenditure is partly constant and partly varies directly with the size of the household, so we can express it as:
Q = k + ds
Now, we can use the given information to find the values of Q, d, and s:
When d = 400 and s = 6, Q = 300.
Substituting the values into the equation:
300 = k + (400)(6)
300 = k + 2400
To find the constant expenditure (k), subtract 2400 from both sides of the equation:
k = 300 - 2400
k = -2100
Therefore, the equation connecting d and s is:
Q = -2100 + ds
To find the equation connecting the total expenditure (Q) with the size of the household (s) and the constant component (d), we need to use the information given.
Let's break down the problem:
1. The total expenditure (Q) is partly constant (d) and partly varies directly with the size of the household (s).
We can represent this as:
Q = d + ks
2. We are given that when Q = 300, d = 400, and s = 6.
Substituting these values into the equation, we get:
300 = 400 + 6k
To solve for the value of k, we need to isolate it. Subtracting 400 from both sides, we have:
300 - 400 = 6k
-100 = 6k
Dividing both sides by 6, we get:
-100/6 = k
-50/3 = k
Now, we have the value of k. Let's substitute it back into the equation:
Q = d + ks
Q = 400 + (-50/3)s
Simplifying, we can write it as:
Q = 400 - (50/3)s
Therefore, the equation connecting the total expenditure (Q) with the size of the household (s) and the constant component (d) is:
Q = 400 - (50/3)s