Question

When a salesperson sells 3 appliances in a month, she is paid $2450.


When a salesperson sells 7 appliances in a month, she is paid $3050.


Let x represent the number of appliances sold in a particular month.


Let y represent the pay for that month.


A. Find the equation of the line that represents this situation.
B. How much would they earn if they sold 11 appliances?



C. How many appliances were sold during the month if she earned $4100?

Answer 1

Solution :

Let, the equation on the line representing the given situation is :

y = mx + c

Here, m is the slope and c is the y-intercept .

Putting, ( 3, 2450 ) in above equation, we get :

2450 = m(3) + c

3m + c = 2450   ...1 )

Also, putting ( 7, 3050 ) in above equation, we get :

3050 = m(7) + c

7m + c = 3050   ...2)

Solving equation 1) and 2) , we get :

4m = 600

m = 150 and c = 2000

So, equation of line will be :

y = 150x  + 2000

A.)

Putting, x = 11 in above equation, we get :

y = ( 150 × 11 ) + 2000

y = $3650

B)

4100 = 150x + 2000

150x = 1100

x = 7.33

Since,  number of appliances sold cannot be in decimals.

So, x = 7

Hence, this is the required solution.