Answer: 1. A) P(c) = 45.5c
2. B) W(x) = 24x
Step-by-step explanation:
1) If the amount of sales p(c) varies directly with the number of customers c, mathematically we have;
p(c) = kc where k is the constant of proportionality
Since ten customers bought a total of $455 worth of sweaters,
p(c) = $455 and c = 10
Substituting this values in the equation we have to get k
$455= 10k
k = $455/10
k = $45.5... (1)
To find the sales p(c) for c customers, we substitute the value of k in the formula
p(c) = kc
p(c) = $44.5c (A)
b) If the time it takes to wash all the windows on a large building W(x) varies inversely with the number of workers assigned to the job x, we will have,
W(x) = k/x (since it is inverse)
If it takes 6 hours to complete the job when 4 workers are assigned to it, the equation becomes;
6= k/4
k = 24... (1)
The equation that can be used to find the time to complete the job when x workers are assigned to it will be;
W(x) = kx
Since k = 24, we will substitute it in the formula to have;
W(x) = 24x which is the required equation (B)
