Question

1. A website sells sweaters. The amount of sales p(c) varies directly with the number of customers c. Ten customers bought a total of $455 worth of sweaters.

Which equation can be used to find the sales for c customers?

A. P(c) = 45.5c
B. P(c) = 455c
C. P(c) = 4550/c
D. P(c) = 455/c

2. 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. It takes 6 hours to complete the job when 4 workers are assigned to it.

Which equation can be used to find the time to complete the job when x workers are assigned to it?

A. W(x) = 1.5x
B. W(x) = 24x
C. W(x) = 10/x
D. W(x) = 24/x

Answer 1

Number 1. is D.
Number 2. is A.
Let me know if they are correct.

Answer 2

Answer: 1. A) P(c) = 45.5c

2. B) W(x) = 24x

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)