Answer:
A) x + y = 24 and 16x + 20y = 434
B) Item A = 11.5 hours per day
Item B = 12.5 hours per day
C) The work done in part A was to derive a system of equations based on the values given to us to produce the items where x and y denoted the number of hours per day it took to make item A and B respectively. Meanwhile, in part B, I employed the substitution method to solve the simultaneous equation derived in part A in order to get the number of hours per day used for each item.
Explanation:
A) Let x represent the amount of hours it took to make item A and let y represent the amount of hours it took to make item B.
Thus, since the machine runs 24 hours a day, we have;
x + y = 24 - - - (eq 1)
Since the plant can make 16 of Item A and 20 of Item B per hour and it made 434 items yesterday, we have;
16x + 20y = 434 - - - (eq 2)
B) to find the time taken for each item per day, let's make x the subject in eq 1.
x = 24 - y
Put 24 - y for x in eq 2;
16(24 - y) + 20y = 434
384 - 16y + 20y = 434
4y = 434 - 384
4y = 50
y = 50/4
y = 12.5 hours
Thus, x = 24 - 12.5
x = 11.5 hours
C) The work done in part A was to derive a system of equations based on the values given to us to produce the items where x and y denoted the number of hours per day it took to make item A and B respectively. Meanwhile, in part B, I employed the substitution method to solve the simultaneous equation derived in part A in order to get the number of hours per day used for each item.