Question

Last week, Hazel paid $32 to have 50 reports printed. This week, she paid $57 to have 100 reports printed. Assume the relationship is linear. Which equation models the relationship between the number of reports,x, and the and the cost, y, ?

Answer 1

Answer: Relationship between the number of reports and the cost of reports printed is given by

$2y-x=14$

Step-by-step explanation:

Let the number of reports be x

Let the cost of report printed be y

Since we have given that for 50 reports he is paid $32

and for 100 reports printed he is paid $57.

So we have (50,32) and  (100,57)

To get the relationship between the number of reports x, and the cost y , we find the slope using two points mentioned above.

As we know the formula for two point slope form :

$m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{57-32}{100-50}\\\\m=\frac{25}{50}\\\\m=\frac{1}{2}$

Now, using the equation of line using two point slope form:

$y-32=\frac{1}{2}(x-50)\\\\2(y-32)=x-50\\\\2y-64=x-50\\\\2y-x=-50+64\\\\2y-x=14$

∴ This is the required relationship between the number of reports and the cost of reports printed.

Answer 2

32y=50x
57y=100x
Simplify:
y=1.5x
y=1.75x