Kevin can make 10 widgets in 7 hours and David can make 12 widgets in 5 hours. How many hours are needed for them to make 67 widgets together?

17.5 hours or 17 h 30 min

Step-by-step explanation:

Kevin makes (10/7) widgets per hour.

David makes (12/5) widgets per hour.

Together they make

(10/7 + 12/5)  widgets per hour.

Also, they make 67 widgets for x hours.

So, they can make 67/x  widgets per hour.

10/7 + 12/5 = 67/x

(10*5)/(7*5) + (12*7)/(5*7) = 67/x

50/35 + 84/35 = 67/x

134/35 = 67/x

134x = 35*67

x = 35*67/134 = 17.5 h

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph