A machine at a manufacturing plant can make 16 of Item A and 20 of Item B per hour. The machine runs 24 hours a day. Yesterday, it made 434 total items. Part A: Write a system of equations to represent this scenario.
Part B: Solve the system of equations for each variable.
Part C: In your own words, write one paragraph explaining the work you did to solve steps A and B.

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.

Step-by-step 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.

answer: 2530

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